Volume contents and author index, volume 13 1989

elm

Theory, Methods & Applications Volume 13, 1989

Pergamon Oxford

- New

York-

Press Beijing

- Frankfurt

Sao Paulo- Sydney-Tokyo-Toronto

NONLINEAR ANALYSIS THEORY, METHODS & APPLICATIONS Editor:

Prof.

Technology,

Editorial

V. Lakshmikantham,

150 West

Secretary:

Umversity Donn

Department of Apphed Boulevard, Melbourne, FL

Mathematics, Florida 32901-6988, USA

Institute

of

Harmsh

HonoraryEditorial Board L Cesart, Untveratty of Mt~h~gan, Ann Arbor, ML USA E A C o d d l n g t o n , Untverwty o[ Cah[ornta, Los Angeles, CA, USA D G K e n d a l l , Cambrtdge Untverstty, Cambrtdge, UK

M A K r a s n o s e l s k n , lnstttute oJ Control Scten(e~, Moscow, USSR J L Lions, Collbge de France, Parts l e, Prance Ju A M l t r o p o l s k n , Dtre~tor o! the lnstttute of Mathematus, Ukramtan SSR )4eademy o/ S(ten(es, Repro Street-3, Kww-4, USSR

L N l r e n b e r g , New York UmversttvCourant, New York, N Y 10012, USA P A S a m u e l s o n , M I T Cambrtdge, MA, USA

Associate Editorial Board A h m a d , Umver~tty of Mtamt, Coral Gableg, FL 33124, USA H A m a n n , Mathematt~che~ lnstttut, Untversttat Zurtch, Ramtstr 74, CH8001 Zurtch, Swttzerland A A m b r o s e t t l , Clasw dt Sctenze, S(uola Normale Super~ore dt Ptsa, Ptazza Det Cavahert 7, 56100, Ptsa, Italy T B BenJamin, Mathematt(al Im'tttute, 2429 St Gdeg, O.rford, UK M S Berger, UmverstO' of Massachusetts, Amherst, MA 01003, USA H Brezis, 4 Place Jussteu, PartL France F E B r o w d e r , Rutgers UmverstO', New Brun~wwk, N J, USA J C h a n d r a , Army Research Office, Durham, NC, US~4 R Contl, Vta G B Amt(t 14/A, 50134, Ftrenze, Ital) G D a P r a t o , Classe dt Sctenze, Seuola Normale Supertore d~ Ptsa, Ptazza Det Cavahert 7, 56100, Ptsa, Ital)' K D e l m h n g , Fa(hberet(h 17 der Gesamthoehschule, Warburger Stras~e 100, D 4790 Paderborn, FRG S

R P Gilbert, Umverstty of Delaware, Newark, DE, USA J K Hale, Center [or Qvnaml(al Systems and Nonhnear Studte~, Georgm Im'tttute o[ Te.ehnolog) , Atlanta, GA 30332, USA T G Hallam, UmverslO' o[ Tenne~ree. Knox'vdle. TN 37916, USA S Leela. State Untvers'tt3 o! New York at Geneseo, NY, USA P - L Lions, Untverwt? de Part~ IXDauphme, plat e de LattredeTaJslgn), 75775 Part~ Cede~ 16, France K Masuda, Department of Mathematt(+, Facul O' of Setenee, Untver~t0 o[ Tokyo, Tokyo, 113, Japan J M a w h l n , Umversttb Cathohque de Louvam, Belgtum R May, Zoolog3 Department, Oxford Umverstty, OMord, OXI 3PS, UK J, B M c L e o d , Wadham College, O~'[ord, UK A Myshkls, Altu[evvcoy Shosw, Mos(o~t, USSR Z N a s h e d , Untver~tty o[ Delaware,

Newark, DE 19716, USA O d e n , Untvers'tty o[ Texas at 4u~ttn, Austin, TX 78712, USA C Olech, Im'O'tut Matematy(zny PAN, Warscawa, Poland P H RablnOWltZ, Mathemattcs Department, UmverstO' of WtwonsmMadt~on, Van Vleek Hall, 480 Ltn(oln Drtve, Madtson, WI 53706, USA W C R h e m b o l t , Department o! Mathematt~ ~ & Stattstt(s, Umverstty o[ Ptttvburgh, Pttt~'burgh, PA 15260, USA E Roxln, Department o/ Mathematt~s, UntverstO' o[ Rhode l~land, Kmgston, RI 02881, USA L Salvadorl, Dtparttmento ch Matemattea, Untversttgt degh Studt dt Trento, 38050 Povo, Trento, Italy M Scott, Sandta Corporatton, Albuquerque, NM, USA R T e m a m , Umver~tt~; de Part~ XI, 91405 Orsay, France C P T s o k o s , Untverstty of Southern Flortda, Tampa, FL. USA W Walter, Untver~ttat Karlsruhe, 75 Karlsruhe. FRG T

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Volume Contents V o l u m e 13 N u m b e r S. K KAUL

1

1

A semi-dynamical system assocmted with a general control

system J.TuRo

7

A boundary value problem for hyperbohc systems of dffferentml-funct~onal equauons

E. N. DANCER

19

A counterexample to the Lazer McKenna conjecture

A. FAVIN1 and P PLAZZI

23

On some abstract degenerate problems of parabohc type--2 The nonhnear case

C CORTAZAR and M. ELGUETA

33

Locahzatlon and boundedness of the solutions of the Neumann problem for a filtration equation

J.DUVALLET

43

A theorem of existence for &scontlnuous &fferenual systems with two point boundary condmons

A. F. ACKER and B KAWOHL

53

Remarks on quenching

J TS1NIAS

63

A Lyapunov description of stabdlty in control systems

S Huand

75

Periodic boundary value problems impulsive dlfferenual systems

87

On some nonconvex varmt~onal hemwarmt~onal mequalmes

V. LAKSHMIKANTHAM Z NAN1EW1CZ

for

second

problems

order

related

to

SOFTWARESU RVEY SECTION

CHEN YUNMEI

V o l u m e 13 N u m b e r 2 101 The hfe span of the solutions to Cauchy problems for nonhnear wave equations

J, M BORWEIN and H M STROJWAS

125

The hypertangent cone

SHEN ZUHE

145

On the perio&c solution to the Newtonlan equahon of motion

m. CAPOZZ1, D LUPO and S SOLIMINI

151

On the existence of a nontnvlal solution to nonhnear problems at resonance

J. M, RAKOTOSON

165

On some degenerate and nondegenerate quasdinear elliptic systems with nonhomogeneous Dmchlet boundary condmon

A. ALVINO, G. TROMBETTI

185

On optimization problems with prescribed rearrangements

and P. L LIONS SOFTWARE SURVEY SECTION

iu

Volume 13 Number 3 K P R SASTRY, S V R NA1DU and J R PRASAD

221

Common fixed points for mulumaps m a metric space

A. STAHEL

231

Hyperbohc mmal boundary value problems with nonhnear boundary condmons

T KACZYNSKIand

259

An applicanon of Ky-Fan fixed point theorem to an optlmlzauon problem

S AHMAD and A C LAZER

263

Asymptouc behavlour of solutions of periodic competmon diffusion system

R P GILBERTand WEN GUO-CHUN

285

Free boundary problems occurring m planar fluid dynamics

P CANNARSA and H. M. SONER

305

Generahzed one-sided estimates for soluuons of Hamilton Jacob~ equauons and appllcatmns

J A GOLDSTEIN, S (~)HARUand T TAKAHASHI

325

Semlhnear Hille-Yoslda theory the approximation theorem and groups of operators

NGUYI~N PHUONG CAC

341

On the number of solutions of an elllptm boundary value problem w~th jumping nonhneanty

V ZEIDAN

SOI~TWARESURVEY SECTION

Volume 13 N u m b e r 4

Au+)tuq-]u]4'l"-2)u=0

DONG ZHANG

353

Onmultlplesolutlonsof

L BOCCARDO, F MURAT

373

Existence results for some quasflinear parabohc equations

YONG-ZHUO CHEN

393

The generahzed degree for compact perturbations of maccreUve operators and apphcatmns

R R[ccI and D A. TARZIA

405

Asymptouc behavior of the soluuons of the dead-core problem

J W NEUBERGER

413

Constructive varlaUonal methods for differential equations

and J-P. PUEL

IV

P. TRACQU1, J. F STAUB and A. M. PERAULT-STAUB

429

Analysis of degenerate H o p f bifurcations for a nonlinear model of calcium metabohsm

L. WHITE and J T. ODEN

459

Dynamics and control of viscoelastic sohds with contact and friction effects

SOFTWARE SURVEY SECTION

Volume 13 Number 5 G. CICOGNA and G GAETA

475

M. S DREW, S C KLOSTER and J. D. GEGENBERG

489

Periodic soluuons from symmetry Lie group analysis and slmdanty solutions for the equation

021,1 02U Ox~-~ + Oy-~

O2(eu) +

OZ 2

--

0

H. IKEOA, M. MIMURA and Y.NISHIURA

507

Global bifurcation phenomena of travelhng wave solutions for some b~stable reaction diffusion systems

KUNG-CHING CHANG

527

On the periodic nonhneanty and the multiplicity of solutions

S RADULESCU and M. RADULESCU

539

Global unlvalence and global reversion theorems m Banach spaces

M.NAKAO

555

On some regularity of peno&c solutions of the wave equation with a nonlinear or degenerate dissipative term

A HARAUX

565

A remark on Holder continuity of periodic solutions to some nonhnear wave equations

V. H. MOLL

569

A note on M c K e a n ' s caricature for nerve conduction

J.-F. LEON and G.TARANTELLO

579

Breaking of symmetry for a minimization problem

YUAN JIANCHENG

589

Necessary and suffioent con&tions for existence of perlo&c solutions of n-dimensional dynamical systems

SOFTWARESURVEY SECTION

Volume

13 N u m b e r

6

N H1RANO

599

Nonlinear evolution perturbations

equations

M A HERRERO

611

A hmlt case in nonlinear dlffUslon

J - P PENOT

629

Metric regularity, openness and Llpschltzlan behavior of multi functions

M S MOULAY and M PIERRE

645

Regularizing effect for a nonlinear diffusion with Irregular source-term

S ELAYDI and S K KAUL

657

Asymptotic stability In general dynamical systems

H EGNELL, F PACELLA and M. TRICARICO

671

Some remarks on Sobolev inequalities

J SANTANILLA

683

Solvability of a nonhnear boundary value problem without Landesman Lazer condition

N. HIRANO

695

Existence of nontrlvlal equations

F. G1ANNONI

707

Periodic solutions of dynamical systems by a saddle point theorem of Rablnowltz

J -B H1RIART-URRUTY and A. SEEGER

721

Calculus rules on a new set--valued second order derivative for convex functions

solutions

with

nonmonotonlc

of semlhnear

elhptlc

SOFTWARE SURVEY SECTION

Volume

13 N u m b e r

7

I.GYORI

739

Existence and growth of oscillatory solutions of first order unstable type delay differential equations

A UNAL

753

An algebraic criterion for the onset of chaos in nonlinear dynamical systems

J. M. FRAILE and

767

General conditions for the existence of a "critical pointperiodic wave front" connection for reaction-&ffUSlOn systems

787

Singular perturbation theory applied to the electrochemistry equations in the case of electroneutrahty

J C SABINA

J. HENRY and B. LOURO

v1

R R. AKHMEROV

803

On periodic travelhng waves of equations with viscosity coefficient of variable sign

V LAKSHMIKANTHAMand XINZHI LIU

819

On quasi stability for impulsive differential systems

HUANG ZHENG MING

829

A necessary and sufficient condition for the existence of a solution to an operator equation

U. LEDZEWICZ-KOWALEWSKA

833

A necessary and sufficient condition for Altman's maximal element problem for constraint sets with many equalities

J. HULSHOF, D. TERMAN and F. VERHULST

841

Existence of stationary solutions in the coronal loop problem

C MARTINEZ-Y,~NEZ

857

A fixed point theorem on k-uniformly rotund spaces

R. SINE

863

Hyperconvexlty and approximate fixed points

R CHIAPPINELLI

871

On spectral asymptotlcs and bifurcation for elliptic operators with odd superhnear term

SOFTWARE SURVEY SECTION

Volume 13 N u m b e r 8 MOHAM MED GUEDDAand

879

Quaslhnear elhptlc equanons exponents

P. J RABIER

903

Generahzed Jordan chains and two bifurcation theorems of Krasnoselskll

A. KLARBRING,A MIKELI(, and M SHILLOR

935

On friction problems with normal comphance

R. MICHALEK

957

A 7/° Borsuk Ulam theorem and index theory with a mulnpllclty result m partial dlfferenual equauons

S. TOIARO

969

Mutual shading effect on algal d~stnbuUon a nonhnear problem

LAURENTVERON

VII

involving crlucal Sobolev

A. BRESSANand A. CORTESI

987

D~rectlonally continuous selecuons in Banach spaces

H I. FREEDMAN and V. TAKEUCHI

993

Global stablhty and predator dynamics m a model of prey &spersal m a patchy environment

SOFTWARE SURVEY SECTION

Volume

13 N u m b e r

9

L. QI

1003

The maximal normal operator space and integration of subdlfferentmls of nonconvex functions

F. A. HOWESand S SHAO

1013

Asymptotic analysis of model problems for a coupled system

P. EABRIE

1025

Regularity of the solution of Darcy Forchhelmer's equation

M. TSUTSUMI

1051

On smooth solutions to the initial-boundary value problem for the nonlinear Schr6dlnger equation in two space dimensions

1. MANDHYAN

1057

Examples of global normal forms for some simple nonlinear Integral operators

E. N BARRONand H. ISHII

1067

The Bellman equation for minimizing the m a x i m u m cost

A -K. DRANGEID

1091

The principle of llnearlzed stabJhty for quaslllnear parabolic evolution equauons

J. DA SILVA FERREIRA

1115

Asymptotic behawor of the solutions of a nonlinear system of Klein-Gordon equations

SOFTWARE SURVEY SECTION

Volume

13 N u m b e r

l0

PRIMO BRANDI and ANNA SALVADORI

1127

On the nonparametrlc integral over a BV surface

J. Q. LIu

1139

Nonlinear vibration of a beam

PIERLUIGI COLLI

1149

On a nonlinear and nonlocal evolution equation related to muscle contraction VII!

HIROYUKI USAMI

1163

On a singular elhpuc boundary value problem in a ball

GIOVANNI VIDOSSICH

1171

On the solvability of boundary value problems for higher order ordmary dffferentml equauons

V LAKSHMIKANTHAMa n d XINZHI LIU

1181

On asymptotxc stability for nonautonomous systems

NOBOYUKI KENMOCHI a n d IRENA PAWLOW

1191

Asymptotic behavlour of solunons to parabohc elhptlc variational mequahtleS

B. H GILDING

1215

Locahzauon of soluuons of a nonhnear Fokker Planck equauon w~th Dmchlet boundary condmons

OLIVIER REY

1241

A multlphoty result for a variational problem with lack of compactness

dffferentml

SOFTWARE SURVEY SECTION

Volume 13 Number 11 PttAM Htr,¢ DIFN a n d PHAM [-IUUSACH

1251

Further properties of the regularity of inclusion systems

F PAC ~RD

1269

Convergence of surfaces of prescribed mean curvature

N S PM'A(,iOR(,I()U

1283

Relaxauon of infinite dimensional control systems

Hllosul ]suu and

1295

A remark on a system of mequallues with bilateral obstacles

('ItlN-YVAN LIN

1303

Degenerate nonlinear parabolic boundary value problems

M KwApisz

1317

On the error evaluation of approximate solutions of discrete equations

F 1 NJOKt and F ZaNOI IN

1329

Posmve solutions multiphclty results

A P MoR(,a, N and

1339

A globally convergent polynomial systems

N \()KIY~MAI) ~.

L T WATSON

IX

for two-point

BVP's

parallel algorithm

existence and

for zeros of

HWAI-CHIUANWANG

1351

The generahzed Strauss compactness lemma and its apphcatmns on nonhnear elliptic problems

B TAN(;

1359

On the existence of periodic solutions m the hmlted Explodator model for the Belousov Zhabotmsku reaction

SOFFWARI St)RVF~ SE(TION

V o l u m e 13 N u m b e r 12 M. G. CRANDALLand P. E SOUGANIDIS

1375

On nonlinear equations of evolution

J. N. GLOVER

1393

Hopf bifurcations at infinity

S. CARL

1399

The monotone iteratwe technique for a parabolic boundary value problem with discontinuous nonlinearity

A ACKER

1409

Uniqueness and monotonlclty of solutions for the interior Bernoulli free boundary problem in the convex, n-dimensional case

B. LAFFERRIEREand W. V. PETRYSHYN

1427

Newposmve fixedpolnt and elgenvalue results forPr-compact maps and some apphcations

B. SCARPELLINI

1441

A class of singular boundary value problems

N. KUTEV

1475

On the solvabdlty of the Dlrlchlet problem for degenerate equations of Monge-Ampere type

SOFTWARE SURVEY SECTION

Title Page, Volume Contents and Author Index, Volume 13, 1989

Author Index Acker, A. 1409 Acker, A.F. 53 Ahmad, S. 263 Akhmerov, R.R. 803 Alvino, A. 185 Barton, E.N. 1067 Boccardo, L. 373 Borwein, J.M. 125 Brandi, P. 1127 Bressan, A. 987 Cannarsa, P. 305 Capozzi, A. 151 Carl, S. 1399 Chen Yunmei i01 Chiappinelli, R. 871 Chin-Yuan Lin 1303 Cicogna, G. 475 Colli, P. 1149 Cortazar, C. 33 Cortesi, A. 987 Crandall, M.G. 1375 Dancer, E.N. 19 Dong Zhang 353 Drangeid, A.-K. 1091 Drew, M.S. 489 Duvallet, J. 43

Glover, J.N. 1393 Goldstein, J.A. 325 Guedda, M. 879 Gyori, I. 739 Haraux, A. 565 Henry, J. 787 Herrero, M.A. 611 Hirano, N. 599, 695 721 Hiriart-Urruty, J.-B. Howes, F.A. 1013 Hu, S. 75 Huang Zheng Ming 829 Hulshof, J. 841 Hwai-Chluan Wang 1351 Ikeda, H. Ishii, H.

507 1067, 1295

Kaczynski, T. 259 Kaul, S.K. I, 657 Kawohl, B. 53 Kenmochi, N. 1191 Klarbring, A. 935 Kloster, S.C. 489 Kung-Ching Chang 527 Kutev, N. 1475 Kwapisz, M. 1317

Fabrie, P. 1025 Favini, A. 23 Fraile, J.M. 767 Freedman, H.I. 993

Lafferriere, B. 1427 Lakshmikantham, V. 75, 819, 1181 Lazer, A.C. 263 Ledzewicz-Kowalewska, U. 833 Leon, J.-F. 579 Lions, P.L. 185 Liu, J.Q. 1139 Louro, B. 787 Lupo, D. 151

Gaeta, G. 475 Gegenberg, J.D. 489 Giannonl, F. 707 Gilbert, R.P. 285 Gilding, B.H. 1215

Mandhyan, I. 1057 Mart~nez-Y~nez, C. Michalek, R. 957 Mikeli~, A. 935 Mimura, M. 507

Egnell, H. Elaydi, S. Elgueta, M.

671 657 33

857

Moll, V.H. 569 Morgan, A.P. 1339 Moulay, M.S. 645 Murat, F. 373 Naidu, S.V.R. 221 Nakao, M. 555 Naniewicz, Z. 87 Neuberger, J.W. 413 4 Nguyen Phuong Cac 341 Nishiura, Y. 507 Njoku, F.I. 1329 Oden, J.T. ~haru, S.

459 325

Pacard, F. 1269 Pacella, F. 671 Papageorgiou, N.S. 1283 Pawlow, I. 1191 Penot, J.-P. 629 Perault-Staub, A.M. 429 Petryshyn, W.V. 1427 Pham Huu Sach 1251 Pham Huy Dien 1251 Pierre, M. 645 Plazzi, P. 23 Prasad, J.R. 221 Puel, J.-P. 373 Qi, L.

1003

Rabier, P.J. 903 Radulescu, M. 539 V Radulescu, S. 539 Rakotoson, J.M. 165 Rey, O. 1241 Ricci, R. 405 Sabina, J.C. 767 Salvadori, A. 1127 Santanilla, J. 683 Sastry, K.P.R. 221 Scarpellini, B. 1441 Seeger, A. 721

Shao, S. 1013 Shen Zuhe 145 Shillor, M. 935 1115 Silva Ferreira, J. da Sine, R. 863 Solimini, S. 151 Soner, H.M. 305 Souganidis, P.E. 1375 Stahel, A. 231 Staub, J.F. 429 Strojwas, H.M. 125 Takahashi, T. 325 Takeuchi, Y. 993 Tang, B. 1359 Tarantello, G. 579 Tarzia, D.A. 405 Terman, D. 841 Totaro, S. 969 Tracqui, P. 429 Tricarico, M. 671 Trombetti, G. 185 Tsinias, J. 63 Tsutsumi, M. 1051 Turo, J. 7 Unal, A. Usami, H.

753 1163

Verhulst, F. 841 Veron, L. 879 Vidossich, G. 1171 Watson, L.T. 1339 Wen Guo-Chun 285 White, L. 459 Xinzhi Liu

819, 1181

Yamada, N. 1295 Yong-Zhuo Chen 393 Yuan Jiancheng 589 Zanolin, F. Zeidan, V.

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