Differential and Difference Equations with Applications: Contributions from the International Conference on Differential & Difference Equations and Applications

639 Pages·2013·5.87 MB·English

by  Ondřej Došlý

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
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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
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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