Lecture Notes in Mathematics Edited by A. Dold and B. Eckmann

703

Equadiff IV Proceedings, Prague, August 22-26, 1977

Edited by Jiri Fabera

Springer-Verlag Berlin Heidelberg NewYork 1979

Editor Jii'f Fabera t Mathematical Institute Czechoslovak Academy of Sciences Zitna 25 11567 Praha 1, Czechoslovakia

Library of Congress Cataloging in Publication Data

Czechoslovak Conference on Differential E~uations and Their Applications, 4th, Prague, 1977. E~uadiff IV.

(Lecture notes in mathematics ; 703) Includes bibliographies and index. 1. Differential e~uations--Numerical solutions--Con­

gresses. 2. Differential e~uations, Partial--Numerical solutions--Congresses. I. Flibera, Jii'i. II. Title. III. Series: Lecture notes in mathematics (Berlin) ; 703. QA3 . L28 no. 703 [QA372] 510' .8s [515' .35]

79-lll03

AMS Subject Classifications (1970): 34A02, 35A02, 65A02, 93A02

ISBN 3-540-09116-5 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-09116-5 Springer-Verlag New York Heidelberg Berlin

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under§ 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher

© by Springer-Verlag Berlin Heidelberg 1979 Printed in Germany

Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2141/3140-543210

PREFACE

The Czechoslovak Conference on Differential Equations and Their Applications - EQUADIFF 4 - was held in Prague from August 22 to August 26, 1977. It continued the tradition of conferences held in Prague (1962), in Bratislava (1966) and in drno (1972). The topic

were differential equations in the broad sense including numerical methods and one of the goals of the conference was to stimulate co­

operation between various branches in differential equations. The conference was organized by the Mathematical Institute of the Cze­choslovak Academy of Sciences in cooperation with the Faculty of Mathematics and Physics of the Charles University in Prague, the Fa­culty of Sciences of the Comenius University in Bratislava, the Czech

Technical University in Prague and the Technical University in Brno. The Organizing Committee was presided by J.Fabera, the members

being O.Bor~vka, J.Brilla, O.Hajkr, J.Kurzweil, I.Marek, J.Moravcik, J.Necas, B.Nov8k, M.Prager, M.Rab, K.Rektorys, M.~vec, O.Vejvoda, M.Zlamal.

The scientific program of the conference comprised 5 invited addresses, 58 invited lectures and 157 scientific communications; the lectures and scientific communications were held simultaneously in three sections:

1. Ordinary Differential Equations, 2. Partial Differential Equations, ). Numerical Methods and Applications.

The participants and their accompanying persons could enjoy a rich social program. The conference was attended by 167 participants from Czechoslovakia and 187 participants from abroad (Austria, Bel­

gium, Berlin-West, Bulgaria, Canada, Egypt, F.R.G., France, G.D.R., Hungary, Italy, Japan, Netherlands, Poland, Roumania, Saudi Arabia,

Sweden, Switzerland, U.S.A., U.S.S.R., United Kingdom, Yugoslavia). The number of accompanying persons was 49.

This volume contains the texts of plenary addresses and of invi­ted lectures which were held in sections -with several exceptions.

We acknowledge the work of Vl.Dolezal, J.Jarnik and P.Prikryl in preparation of this volume.

Editors

LIST OF INVITED ADDRESSES

Plenary Session

Borllvka, o.

Everitt, W.N.

Marek, I.

Necas, J.

Oleinik, O.A.

Algebraic methods in the theory of glo­bal properties of the oscillatory equa­tions Y" = Q(t)Y Singular problems in the calculus of variations and ordinary differential equations Eigenvalues and bifurcations in reactor physics and chemistry On the existence and regularity of weak solutions to varia~ional equations and inequalities Energeticeskije ocenki, analogicnyje principu Saint-Venant i ich prilozenija

Ordinary differential equations

Antosiewicz, H.A.

Bainov, D.D.: Bainov, D.D. and Milusheva, S.D.

aebernes, J.W.

Bihari, I.

Blagodatskich, V.

Coddington, E.A.

Conti, .H. Gamkrelidze, .H.V.

Halanay, A.

Kamenskii, G.A.: Kamenskii, G.A. and Myshkis, A.D.

Kiguradze, I.T.

Some remarks on the solution of boun­dary value problems

Application of the averaging method for solving boundary problems for ordi­nary differential and integrodifferen­tial equations (Presented by D.D.Bainov) Invariance and solution set properties for some nonlinear differential equa­tions Asymptotic invariant sets of some non­linear autonomous systems of differen­tial equations Some problems in the theory of diffe­rential inclusions Differential subspaces associated with pairs of differential operators Control and the Van der Pol equation Exponential representation of solutions of ordinary differential equations Singular perturbations and linear feed­back control

Variational and boundary problems for differential equations with deviated argument (Presented by A.D.Myshkis) 0 kolebljuscichsja i monotonnych rese­nijach obyknovennych differencial'nych uravnenij

Knobloch, H.W.

Mawhin, J.

Milusheva, S.D.: Bainov, D.D. and Milusheva, S.D.

Myahkis, A.D.: Kamenskii, G.A. and Myshkis, A.D.

Neuman, F.

Olech, c.

Pliss, V.A.

Ryabov, Yu.

Schwabik, ~.: Schwabik, ~. and Tvrdj, M.

~eda, v. ~vee, M.

Tvrdj, M.: Schwabik, ~. and Tvrdj, M.

Vrkoc, I.

VI

Boundary value problems for systems of nonlinear differential equations New results on nonlinear perturbations of linear noninvertible mappings and applications to differential equations

Application of the averaging method for solving boundary problems for ordi­nary differential and integrodifferen­tial equations (Presented by D.D.Bainov)

Variational and boundary problems for differential equations with deviated argument (Presented by A.D.Myshkis) Global properties of the nth order linear differential equations Lower semicontinuity of integral func­tionals Invariantnyje mnozestva periodiceskich sistem differencial'nych uravnenij Ogranicennye operatory v teorii obyk­novennych differencial'nych uravnenij

Linear problems in the space BV (Presented by ~.Schwabik) On de la Vallee Poussin problem Some problems concerning the functional differential equations

Linear problems in the space BV (Presented by ~.Schwabik) A new definition and some modifications of Filippov's cone

Partial differential equations

~ann, H.

Bojarski,

Drozzinov,

DUmmel, s.

Fucik, s. Gajewski,

Hall, w.s.

B.

J.N.

H.

Invariant sets for semi-linear parabo­lic and elliptic systems Overdetermined non-linear systems of partial differential equations and ge­neral quasiconformal mappings Tauberovy teoremy v kompleksnoj plos­kosti i nekotorye ich primenenija On some inverse problems for partial differential equations Nonlinear boundary value problems On the iterative solution of some non­linear evolution equations Monotone operators and the two-time method

Hansen, W. Hess, P.

Kluge, R.

Kral, J. Kuf'ner, A.

Ladyzenskaja, O.A.

Mosco, v.

Rabinowitz, P.H.

Sova, M.

Triebel, H.

VII

On the Dirichlet problem Existence and multiplicity results f'or nonlinear perturbations of' linear ellip­tio and parabolic problems at resonance On the determination of' parameter func­tions in partial dif'ferential equations Boundary behavior of potentials Some modif'ications of' Sobolev spaces and boundary value problems On formulations and solvability of boundary value problems for incompres­sible fluids in domains with noncompact boundaries Dual estimates and regularity of solu­tions of some quasivariational inequali­ties Free vibrations for a nonlinear wave equation Laplace transf'orm and linear differen­tial equations in Banach spaces Strongly degenerate elliptic dif'feren­tial operators

Numerical methods and applications

Axelsson, 0.

deckert, H.

Brilla, J.

Capriz, G.

Descloux, J.: Descloux, J., Nassif, N. and Rappaz, J.

Hlavacek, I.

Il' in, V.

Kacur, J.

Klotzler, R.

On the numerical solution of nonlinear partial differential equations on di­vergence form Remarks on dynamic and static stability theory in nonlinear mechanics Stability problems in mathematical theory of viscoelasticity On the branching of' solutions and Signorini's perturba"ion procedure in elasticity

Numerical approximation of the spectrum of linear operators (Presented by J. Descloux) Dual finite element analysis for uni­lateral boundary value problems Conjugate gradient alternating direc­tion methods for difference equations Application of Rothe's method to non­linear parabolic boundary value pro­blems On a general conception of duality in optimal control

Mika, J.

Nashed, M.Z.

Nassif, N.: Descloux, J., Nassif, N. and Happaz, J.

Nedelec, J.c.

Nedoma, J.

Nohel, J.A.

Rappaz, J.: Descloux, J., Nassif, N. and Rappaz, J.

Raviart, P.A.

Rektorys, K.

Stetter, H.J.

Sultangazin, U.M.

Taufer, J.: Taufer, J. and Vitasek, E.

Vitasek, E.: Taufer, J. and Vitasek, E.

Zlamal, M.

VIII

Asymptotic methods for the singularly perturbed differential equations in Banach spaces Iterative and projection methods for illposed boundary-value problems and operator equations

Numerical approximation of the spectrum of linear operators (Presented by J. Descloux) Finite element approximations of sin­gular integral equations The solution of parabolic models by fi­nite element space and A-stable time discretization Volterra integrodifferential equations for materials with memory

Numerical approximation of the spectrum of linear operators (Presented by J. Descloux) Mixed finite element approximations of the Navier-Stokes equations Approximations of very weak solutions of the first biharmonic problem for multiply connected regions The principle of defect correction and its application to discretization me­thods Issledovanie resenij simmetriceskich polozitel'nych sistem metodom sferi­ceskich garmonik

Numerical solution of evolution pro­blems in Banach spaces (Presented by E.Vitasek)

Numerical solution of evolution pro­blems in Banach spaces (Presented by E.Vitasek) Superconvergence in the finite element method

Angelov, v.

Aulbach, B.

Bobrowski, D. Brjuno, A.D.

Brown, R. c.

Brunovsky, P.

Canturija, T.

Cerha, J. Chow, S. Danes, J.

Dijksma, A. Djaja, c. Dolezal, J.

Elbert, !...

Erbe, L.

~·arkas, M.

Gil'derman, J. Golokvoscjus, P.

Habets, P. Heil, E.

Hetzer, G.

Hristova, s.

LIST OF COMMUNICATIONS

Ordinary differential equatione

Suscestvovanije i edinstvennost resenija na­calnoj zadaci dla odnogo klassa differencial'­nych uravnenij nejtralnogo tipa The method of Zubov in the case of an asympto­tically stable limit cycle On oscillation criteria Normal'naja forma i bifurkacii v dinamiceskich sistemach Boundary value problems with general side con­ditions and their applications On the existence of regular synthesis of the optimal control 0 nekotorych teoremach sravnenija dla obykno­vennych differencial'nych uravnenij Dirac function in Volterra equations Generalized Hopf bifurcation On positive solutions of nonlinear operator equations On ordinary differential subspaces Nekotoryje svojstva kvasi-pocti periodiceskich dvizenij dinamiceskich sistem On a certain type of discret·e two-point boun­dary value problem arising in discrete optimal control A comparison theorem for first order nonlinear differential equations with delay Some applications of change-of-variable tech­niques for linear differential equations Estimates on the existence regions of pertur­bed periodic solutions Kusocno-afinnyje dinamiceskije sistemy 0 strukture integralnoj matricy odnoj dvumer­noj sistemy differencial'nych uravnenij v okrestnosti regularnoj osoboj tocki sistemy On relaxation oscillations On an oscillation criterion of Hartman­-Wintner-Potter Some remarks on periodic solutions of second order systems of ordinary differential equa­tions Asimptoticeskoje razlozenije resenija odnoj nacalnoj zadaci o singularno vozmuscennoj sis­teme integro-differencial'nych uravnenij s zapazdyvanijem

J~dryka, T.M.

Kappel, 1!,.

Karim, R.I.

Kartak, K.

Kisielewicz, M.

Komornik, J.

Krbec, P. Kvedaras, B.

Kwapisz, M.

Laloux, B. Mallet-Paret, J. Marusiak, r.

Medved, M.

Mikulik, z.

Miluseva, s.

Mirica, s.

Muldowney, J .s. Muller-Pfeiffer, E.

Myjak, J.

Nikolova, T.S.

Norkin, S.B.

Peitgen, H.-0. Pelczar, A.

X

An estimation of the solution of Volterra integral equation for vector-valued function with values in an Orlicz space (a generaliza­tion of a problem of T.Wa~ewski) Approximation results and functional-differen­tial equations On the resonance case in systems of nonlinear differential equations with periodic coeffi­cients Linear differential equations with disconti­nuous coefficients Extension of the Antosiewicz and Cellina con­tinuous selection theorem Solution of functional equations of the Ricca­ti type on the infinite interval Discontinuous Liapunov functions On the solutions of degenerate differential equations in Banach spaces On the existence and uniqueness of integrable solutions of functional equations in a Banach space Bifurcation problems Global Hopf bifurcation Cscillatory and asymptotic properties of delay differential equations On generic bifurcations of second order ordi­nary differential equations near closed orbits " Uber Transformationen der Differentialgleichun-gen dritter Ordnung Obosnovanije casticno-multiplikativnogo usred­nenija dla resenija krajevych zadac dla dif­ferencial'nych uravnenij s otklonjajuscimsja argument om A suboptimal feedback control for linear slow­-varying systems Linear differential inequalities Stetige Spektren bei Sturm-Liouvilleschen Operatoren Most monotone operators over an invariant set have asymptotic equilibrium Ob odnoj krajevoj zadace dla beskonecnych sis­tern differencial'nych uravnenij s otklonjaju­scimsja argumentom Struktura resenij sistemy differencial'nych uravnenij s zapazdyvajuscimsja argumentom Leray endomorphisms and cone mappings Stability and limit sets in generalized dyna­mical systems

P£a:t:t, R.

Pivovarov, I.

Rasvan, v.

Rejnf'el'd, G. Risito, c. Ronveaux, A.

Rze!uchowski, T.

Schneider, K.R. Sell, G.R.

Stankovic, B.

Vanderbauwhede, A.

Voracek, J.

Vosmansky, J.

Werbowski, J.

Zalinescu, c.

Anger, G.

Bartak, J.

Bernardi, M.L. Biroli, M. Borzymowski, A.

Chabrowski, J.

Doktor, A.

Doktor, P.

XI

Lineare Dif'ferentialgleichungen zweiter Ord­nung mit Distributionskoe:ffizienten A contribution to the structure o:f autonomous nonlinear di:fferential equations Some results concerning the dynamics of' steam turbines control systems Teorema svedenija Asperiodicity criteria Stability interval :for periodic 2nd order differential equation and poles of the Riccati equation An existence theorem for non-convex orientor :fields in a Banach space On Hop:f bifurcation Omega limit sets for flows generated by :functional-differential equations Linear differential equation with coefficients in a ring Symmetric perturbations of nonlinear equations: symmetry of small solutions On a nonlinear differential equation of the third order Certain higher monotonicity properties of li­near differential equations On the asymptotic behaviour of' the solutions of nonhomogeneous differential equation with delay On an abstract control problem

Partial differential equations

Uniquely determined mass distributions in inverse problems Remark on Lyapunov stability of differential equations in Hilbert spaces On some singular evolution equations Homogenization for variational inequalities The uniqueness of solutions of tangential­-derivative problems for some systems of non­linear parabolic equations Local Fatou property for the solution of para­bolic equations Global solution of mixed problem for nonlinear system of conservation laws Remark about perturbations of variational in­equalities

Dragieva, N.A.

Gajewski, H.: Gajewski, H. and Zacharias, K. GOhde, D.

Goncerzewicz, J.

Grabmuller, H.

Hernandez, J.

Herrmann, L.

Holanova-Radochova, v.

Jager, w.

Jarusek, J.

Jasnj, M.

Kerener, R. Kolom,Y, J.

Konig, M.

Kucera, M.

Li tewska, K. Lovicar, v.

Marcinkowska, H.

Maelennikova, V.N.

Musial, I.

Muszynski, J. Naumann, J. Netuka, I.

XII

Une solution de l'equation parabolique dans un domaine non cylindrique

On Vlasov's equation (Presented by K.Zacharias) Eine Klasse singular gestorter elliptischer Differentialgleichungen On the weak solution of boundary value problem arising in theory of water percolation Singular perturbations in linear integra­-differential equations Positive solutions for a class of nonlinear eigenvalue problems Periodic solutions to abstract differential equations Remark to the solution properties of some class of partial differential equations in the di­stributions space A maximum principle and a uniqueness result for solutions of elliptic equations on Rie­mannian manifolds Ranges of certain type of nonlinear operators with applications in partial differential equa­tions Walter's method of lines applied to the equa-tion uw!()x = w'(x) + vVWD 2w! 0 t 2

On nonlinear degenerate parabolic equations Structure of Banach spaces and solvability of nonlinear equations Zur Abschatzung der Losung des Dirichletschen Aussenraumproblems fur die Schwingungsglei­chung Eigenvalue problem for variational inequali­ties Rothe methods for parabolic systems Periodic solutions of second order equations with dissipative terms On a class of mixed problems for linear hyper­bolic equations Asimptoticeskije svojstva resenij sistem gid­rodinamiki vrascajuscejsja zidkosti Some problems of behaviour of solutions in Hilbert apace About some integral equation On a class of integra-differential equations Potentials and boundary value problema for the heat equation

Okrasinski 1 w.

Ptasnik 1 B.

Sadkowski 1 W.

Schappacher, W.

Schoenenberger­-Deuel, J.

Schulze, B.-w.

Skrypnik 1 I. V.

Sosulski 1 W.

Soucek, J. Stara, J.

Straskraba, I.

Szarski, J.

Szep, A. Tabisz, K.

Telschow, G.

Torelli, A. Vaillancourt, F.

Vesely, J. Yamaguchi, M.

von Wolfersdorf, L.

Zacharias, K.: Gajewski, H. and Zacharias, K.

XIII

On nonnegative solutions of a nonlinear con­volution equation occuring in the theory of water percolation "Non-classical" boundary value problems for systems of hyperbolic integra-differential equations Behaviour of solutions of some mixed boundary­-value problem Nonlinear functional differential equations and semigroups

Nonlinear parabolic boundary value problems with upper and lower solutions On elliptic pseudo-differential operators and boundary value problems Koercitivnyje ocenki dla par linejnych ellip­ticeskich operatorov i ich primenenija On convergence of successive approximations of some integral equations On the cartesian minimal surfaces Remark to regularity properties of weak solu­tions On a higher order abstract differential equa­tion Cauchy problem for infinite systems of func­tional-differential equations Singular partial differential equations On the parabolic quasi-variational inequality with unknown boundaries An iteration procedure for control problems with elliptic equations An evolution free boundary problem Application of a theorem of Brezis-Nirenberg to measure-preserving vectorfield on the two­-dimensional torus Some remarks on Dirichlet problem Bounded and almost periodic solutions of qua­silinear wave equations A modification of the Dirichlet variational problem

On Vlasov•s equation

Numerical methods and applications

Abesser, H. Sufficient conditions of optimality and field theory for control problems

Adler, G.

Agol:lkov, v.

Bock, I.

Burda, P. aermB.k, J.

Chocholaty, P.: Chocholaty, P. and ~lahor, r..

David, A.

Desperat, T.

Dryja, M.

Farzan, R.

Feistauer, M.

Galantai, A.

Georg, K.

Godlewski, E.: Godlewski, E. and Raoult, A.P.

Griepentrog, E.

Groger, K.

Haslinger, J.

Kafka, J.M.

Kodnar, R.

Kuznecov, Ju.: Kuznecov, Ju. and Macokin, A.

Lelek, V.: Lelek, v. and ~afar, J.

XIV

Problems in the digital simulation of' thermal secondary oil recovery by combustion Ispol'zovanie variacionnoj f'ormy tozdestva G.I.Marcuka dla resenija nekotorych dif'f'eren­cial'nych uravnenij Bending of' viscoelastic plates with aging Finite elements and diffusion equations Floquet's theory and neutron transport in a periodic slab lattice

A remark on the solution of a boundary value problem with delay (Presented by r..~lahor) Orthonormal systems in quasiparabolic diffe­rential equations Free boundary problems in the theory of fluid flow through porous media Alternating-direction Galerkin method for Navier-Stokes equation Nekotoryje uslovija dla schodimosti i ustoj­civosti cislennogo resenija krajevoj zadaci dla paraboliceskogo uravnenija so slaboj neli­nejnost'ju On the study of' subsonic rotational flow of' an ideal gas On the extensions of' some stiff' stability concept Unstable solutions of' second order nonlinear boundary value problems

Multistep methods for u" + Bu'+ Au = f (Presented by E.Godlewski) Onestep methods for stiff differential equa­tions Evolution equations in the theory of plasti­city Dual finite element analysis of variational inequalities Seventh contribution to the numerical solution of parabolic partial differential equations Uravnenija uprugo-plasticeskich plastinok pri bol'sich progibach

Metod fiktivnych oblastej i ego primenenija (Presented by A.Macokin)

Numerical solution of diffusion equations on nonuniform net (Presented by J.~afar)

Lelek, V.: Lelek, v. and W1esner, J.

Lovisek, J.

Macokin, A.: Kuznecov, Ju. and Macokin, A.

Malina, L. Milota, J.

Moszynski, K. Nasr, H.

Opitz, G.

Pf'ei:t'er, E.

Podhajecky, G.

Prager, M.

Prossdor:t', s.

Raoult, A.P.: Godlewski, E. and Raoult, A.P.

Rvacev, V.L.

~afar, J.: Lelek,V. and ~afar, J.

Sapagovas, M.

vom Scheidt, J. Segeth, K.

~lahor, L.: Chocholaty, P. and ~lahor, L.

Stoyan, G.

XV

Problem of' eigenvalues of' nonsel:t'adjoint Schrodinger operator (Presented by J.Wiesner) A finite element analysis for the Signorini problem in plane elastostatics

Metod :t'iktivnych oblastej i ego primenenija (Presented by A.Macokin) Some remarks on carry over methods Minimal interpolation in Banach spaces (Ge­neral spline functions) Remarks on ~pectral approximation Generalized periodic overimplicit multistep methods for solution of' ordinary differential equations An effective way of generating linear multi­step expressions for ordinary differential equations with arbitrary sequences of step­-size On the discrete convergence of approximate solutions for nonlinear two-point boundary value problems On an algorithm for solving problems of Schwarz's type A remark to the approximate solution of' the Laplace equation in polar coordinates 0 priblizennom resenii nekotorych integral'­nych i integro-di:t':t'erencial'nych uravnenij

Multistep methods for u" + Bu' + Au = f (Presented by E.Godlewski) Algebrologiceskij metod R-:t'unkcij v krajevych zadacach dla oblastej sloznoj formy

Numerical solution of diffusion equations on nonuniform net (Presented by J.~afar) Numerical solution and application of' the drop shape equation Stochastische Eigenwertprobleme Evaluation of convolution integrals in the implementation of the finite element method

A remark on the solution of a boundary value problem with delay (Presented by L.~lahor) A monotone difference scheme for diffusion convection problems allowing for small di:t':t'u­sity

Stye, T.

Szepesvari, I.

Szymanska­-Kol:odziej, D.

Vajtersic, M.

Vetluckij, V.

ViSnlik, K. Wiesner, J.: Lelek, V. and Wiesner, J.

~enisek, A. Zezula, R.

XVI

The method of lines for degenerate nonlinear parabolic equations Error-estimation for certain nonlinear para­bolic equations

Primenenije nekotorogo integral'nogo predsta­vlenija dla resenija sistem uravnenij soder­zascich v sebe uravnenija vtorogo porjadka ellipticeskogo i paraboliceskogo tipov Fast algorithm for numerical solution of bi­harmonic problems on the rectangular region Postanovka i resenije zadaci o vjazkom tece­niji v uzkom kanale Some efficient methods for stiff systems

Problem of eigenvalues of nonselfadjoint Schrodinger operator (Presented J.Wiesner) Curved triangular finite em-elements On some nonlinear problems in reactor optimi­zation

CONTENTS

Amann, H.: Invariant sets for semilinear parabolic and elliptic systems 1

Axelsson, o.: On the numerical solution of nonlinear partial differential equations on divergence form 5

Bainov, D.D. and Milusheva, S.D.: Application of the aver­aging method for the solution of boundary problems for ordinary differential and integro-differential equations 16

Bebernes, J.W.: Solution set properties for some nonlinear parabolic differential equations 25

Bihari, I.: Asymptotic invariant sets of autonomous diffe-rential equations 31

Boruvka, 0.: Algebraic methods in the theory of global pro-perties of the oscillatory equations Y"=Q(t)Y 35

Brilla, J.: Stability problems in mathematical theory of viscoelasticity 46

Capriz, G.: On the branching of solutions and Signorini's perturbation procedure in elasticity 54

Coddington, E.A.: Differential subspaces associated with pairs of ordinary differential operators 64

Conti, R.: Control and the Vander Pol equation 73

Descloux, J., Nassif, N. and Rappaz, J.: On properties of spectral approximations 81

Dragan, v. and Halanay, A.: Singular perturbations and linear feedback control 86

DUmmel, s.: On some inverse problems for partial differen-tial equations 93

Fucik, s.: Nonlinear noncoercive boundary value problems 99

Gajewski, H.: On the iterative solution of some nonlinear evolution equations 110

Gamkrelidze, R.: Exponential representation of solutions of ordinary differential equations 118

Hall, W.S.: The Rayleigh and Vander Pol wave equations, some generalizations 130

Hansen, W.: The Dirichlet problem 139

Hess, P.: Multiple solutions of some asymptotically linear elliptic boundary value problems 145

Hlavacek, I.: Dual finite element analysis for some unilateral boundary value problems 152

Il'in, v.: Gradient alternating-direction methods 160

Kacur, J.: Nonlinear parabolic boundary value problems with the time derivative in the boundary conditions 170

XVIII

Kamenskii, G.A. and Myshkis, A.D.: Variational and boundary value problems £or di£ferential

Klotzler,

Knobloch,

equations with deviating argument R.: On a general conception of duality in optimal control

H.W.: Boundary value problems £or systems o£ nonlinear di££erential equations

Kral, J.: Boundary behavior o£ potentials Ku£ner, A.: Some modi£ications o£ Sobolev spaces and

non-linear boundary value problems Kyncl, J. and Marek, I.: Some problems in neutron

transport theory Ladyzenskaja, O.A.: On £ormulation and solvability o£

boundary value problems £or viscous incom­pressible £luids in domains with non-compact

179

189

197 205

213

224

boundaries 233 Mawhin, J.: Boundary value problems at resonance £or

vector second order nonlinear ordinary di££erential equations 241

Maz'ya, V.G.: Behaviour o£ solutions to the Dirichlet problem £or the biharmonic operator at a boundary point 250

Mika, J.: Asymptotic methods £or singularly perturbed li-near di£ferential equations in Banach spaces 263

Mosco, u.: Non-linear quasi variational inequalities and stochastic impulse control theory 271

Necas, J.: On the regularity of weak solutions to variational equations and inequalities for nonlinear second order elliptic systems 286

Nedoma, J.: The solution of parabolic models by finite element space and A-stable time discretization 300

Neuman, F.: Global properties o£ the nth order linear differential equations 309

Nohel, J.A.: A forced quasilinear wave equation with dissipation 318

Oleinik, O.A.: Energetic estimates analogous to the Saint-Venant principle and their applications 328

Rabinowitz, P.H.: A priori bounds for a semilinear wave equation 340

Rektorys, K.: The method of least squares on the boundary and very weak solutions of the first biharmonic problem 348

Ryabov, Yu.: Application of bounded operators and Lyapunov's majorizing equations to the analysis of differential equations with a small parameter 356

Schwabik, ~. and Tvrey, M.: On linear problems in the space BV 366

~eda,

Sova,

v.: A partially ordered space connected with the de la Vallee Poussin problem

M.: Abstract CauchY problem

374 384

XIX

Sultangazin, U.M.: Solution of symmetric positive systems of differential equations

~vee, M.: Some problems concerning the functional differential equations

Taufer, J. and Vitasek, E.: A-stability and numerical solution of abstract differential equations

Triebel, H.: Mapping properties of regular and strongly degenerate elliptic di~ferential operators in the Besov spaces B (11). p,p The case 0 < p < oo

Vrkoc, I.: A new definition and some modifications of Filippov cone

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