Differential and Difference Equations with Applications: Contributions from the International Conference on Differential & Difference Equations and Applications PDF
Preview Differential and Difference Equations with Applications: Contributions from the International Conference on Differential & Difference Equations and Applications
Springer Proceedings in Mathematics & Statistics Sandra Pinelas Michel Chipot Zuzana Dosla Editors Diff erential and Diff erence Equations with Applications Contributions from the International Conference on Diff erential & Diff erence Equations and Applications Springer Proceedings in Mathematics & Statistics Volume 47 Forfurthervolumes: http://www.springer.com/series/10533 Springer Proceedings in Mathematics & Statistics Thisbookseriesfeaturesvolumescomposedofselectcontributionsfromworkshops and conferences in all areas of current research in mathematics and statistics, includingORandoptimization.Inadditiontoanoverallevaluationoftheinterest, scientific quality, and timeliness of each proposal at the hands of the publisher, individual contributions are all refereed to the high quality standards of leading journals in the field. Thus, this series provides the research community with well-edited, authoritative reports on developments in the most exciting areas of mathematicalandstatisticalresearchtoday. Sandra Pinelas • Michel Chipot • Zuzana Dosla Editors Differential and Difference Equations with Applications Contributions from the International Conference on Differential & Difference Equations and Applications 123 Editors SandraPinelas MichelChipot DepartamentodeCieˆnciasExactas Institutfu¨rMathematik AcademiaMilitar UniversityofZu¨rich Amadora,Portugal Zu¨rich,Switzerland ZuzanaDosla DepartmentofMathematics MasarykUniversity Brno,CzechRepublic ISSN2194-1009 ISSN2194-1017(electronic) ISBN978-1-4614-7332-9 ISBN978-1-4614-7333-6(eBook) DOI10.1007/978-1-4614-7333-6 SpringerNewYorkHeidelbergDordrechtLondon LibraryofCongressControlNumber:2013945534 Mathematics Subject Classification (2010): 33C45, 34-XX, 35-XX, 37-XX, 39A10, 39A13, 39A06, 39A12,45J05,47-XX,54C60,65-XX,76H05,76Z05,92D25,93B03,93B40 ©SpringerScience+BusinessMediaNewYork2013 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’slocation,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer. PermissionsforusemaybeobtainedthroughRightsLinkattheCopyrightClearanceCenter.Violations areliabletoprosecutionundertherespectiveCopyrightLaw. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. While the advice and information in this book are believed to be true and accurate at the date of publication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityfor anyerrorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,with respecttothematerialcontainedherein. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface For five days from July 4 to 8, 2011, more than 230 mathematicians from 50 countries attended the International Conference on Differential and Difference EquationsandApplications,heldatAzoresUniversity,PontaDelgada,Portugal. This conference was held in honour of Professor Ravi P. Agarwal for his contributionstoscienceand,inparticular,tothemathematicalcommunity. The scientific aim of this conference was to bring together mathematicians working in various disciplines of differential and difference equations and their applications. There were 11 plenary lectures, 21 main lectures, and 198 commu- nicationsaboutthecurrentresearchinthisfield.Thisvolumecontains60selected original papers which are connected to research lectures given at the conference. Eachpaperhasbeencarefullyreviewed. We take thisopportunityto thankall the participantsof the conferenceandthe contributors to these proceedings. Our special thanks belong to the Department of Mathematics, Azores University, Ponta Delgada, Portugal, for the sincere hospitality. We are also grateful to the Scientific and Organizing Committees for alltheeffortinthepreparationoftheconference. We hope that this volume will serve researchersin all fields of differentialand differenceequations. Amadora,Portugal SandraPinelas Zu¨rich,Switzerland MichelChipot Brno,CzechRepublic ZuzanaDosla v Contents PartI MainSpeakers Two-TermPerturbationsinHalf-LinearOscillationTheory................ 3 OndˇrejDosˇly´ andSimonaFisˇnarova´ CapillaryForcesonPartiallyImmersedPlates............................... 13 RobertFinn Singular Problems for Integro-differentialEquations inDynamicInsuranceModels.................................................. 27 TatianaBelkina,NadezhdaKonyukhova,andSergeyKurochkin Oscillatory Properties of Solutions of Generalized Emden–FowlerEquations....................................................... 45 R.Koplatadze OnConformingTetrahedralisationsofPrismaticPartitions................ 63 SergeyKorotovandMichalKˇr´ızˇek SwarmDynamicsandPositiveDynamicalSystems.......................... 69 UlrichKrause Periodic Solutionsof DifferentialandDifferenceSystems withPendulum-TypeNonlinearities:VariationalApproaches.............. 83 JeanMawhin Two-DimensionalDifferentialSystems with Asymmetric PrincipalPart..................................................................... 99 FelixSadyrbaev HyperbolicityRadiusofTime-InvariantLinearSystems ................... 113 T.S.Doan,A.Kalauch,andS.Siegmund vii viii Contents OscillationCriteria for Delay and Advanced Difference EquationswithVariableArguments........................................... 127 I.P.Stavroulakis Positive Solutions of Nonlinear Equations with Explicit DependenceontheIndependentVariable..................................... 147 J.R.L.Webb ExistenceResultsforaSystemofThird-OrderRightFocal BoundaryValueProblems ...................................................... 165 PatriciaJ.Y.Wong ForcedOscillationofSecond-OrderImpulsive Differential EquationswithMixedNonlinearities.......................................... 183 A.O¨zbekler,andA.Zafer FromthePoincare´–BirkhoffFixedPointTheoremtoLinked TwistMaps:SomeApplicationstoPlanarHamiltonianSystems........... 197 AnnaPascolettiandFabioZanolin PartII Contributions PullbackAttractorsforNonAutonomousDynamicalSystems.............. 217 Mar´ıaAnguiano,Toma´sCaraballo,Jose´ Real,andJose´ Valero UniformEstimatesandExistenceofSolutionswithPrescribed DomaintoNonlinearThird-OrderDifferentialEquation................... 227 IrinaAstashova ASecond-OrderDifferenceSchemeforaSingularlyPerturbed Reaction-DiffusionProblem .................................................... 239 BasemS.Attili ParametricDependenceofBoundaryTraceInequalities.................... 249 GilesAuchmuty OnPropertiesofThird-OrderFunctionalDifferentialEquations ......... 255 BlankaBacul´ıkova´andJozefDzˇurina OntheStructureofTwo-LayerCellularNeuralNetworks ................. 265 Jung-ChaoBan,Chih-HungChang,andSong-SunLin LinearIntegralEquationswithDiscontinuousKernelsandthe RepresentationofOperatorsonRegulatedFunctionsonTimeScales..... 275 LucianoBarbanti,BereniceCamargoDamasceno,GeraldoNunes Silva,andMarciaCristinaAndersonBrazFederson StrongSolutionstoBuoyancy-DrivenFlowsinChannel-Like BoundedDomains................................................................ 283 MichalBenesˇ Contents ix Infinite-HorizonVariationalPrinciplesandAlmostPeriodic Oscillations........................................................................ 293 Joe¨lBlotandAbdelkaderBouadi ANoteonEllipticEquationsInvolvingtheCriticalSobolevExponent.... 311 GabrieleBonanno,GiovanniMolicaBisci,andVicen¸tiuRa˘dulescu Sign-ChangingSubharmonicSolutionstoUnforcedEquations withSingularφ-Laplacian...................................................... 321 AlbertoBoscagginandMaurizioGarrione Nonlinear Difference Equations with Discontinuous Right-HandSide.................................................................. 331 PasqualeCanditoandRobertoLivrea PullbackAttractorsofStochasticLatticeDynamicalSystems withaMultiplicativeNoiseandNon-LipschitzNonlinearities.............. 341 Toma´sCaraballo,FranciscoMorillas,andJose´ Valero Discrete-TimeCounterpartsofImpulsive HopfieldNeural NetworkswithLeakageDelays................................................. 351 HaydarAkc¸a,Vale´ryCovachev,andZlatinkaCovacheva ASymmetricQuantumCalculus............................................... 359 ArturM.C.BritodaCruz,Nata´liaMartins,andDelfimF.M.Torres StabilityofNonlinearDifferentialSystemswithRight-Hand SideDependingonMarkov’sProcess ......................................... 367 IradaDzhalladova OscillationofThird-OrderDifferentialEquationswithMixed Arguments ........................................................................ 375 JozefDzˇurinaandBlankaBacul´ıkova´ OnEstimatesfortheFirstEigenvalueoftheSturm–Liouville ProblemwithDirichletBoundaryConditionsandIntegralCondition .... 387 SvetlanaEzhak Boundary Value Problems for Schro¨dinger Operators onaPathAssociatedtoOrthogonalPolynomials............................. 395 A.Carmona,A.M.Encinas,andS.Gago CentersinaQuadraticSystemObtainedfromaScalarThird OrderDifferentialEquation.................................................... 405 AdrianaBuica˘,IsaacA.Garc´ıa,andSusannaMaza Three Solutions for Systems of n Fourth-Order Partial DifferentialEquations........................................................... 411 ShapourHeidarkhani
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