简介：TheKurzweil-HenstockintegralformalismisappliedtoestablishtheexistenceofsolutionstothelinearintegralequationsofVolterra-typewherethefunctionsareBanach-spacevalued.SpecialtheoremsonexistenceofsolutionsconcerningtheLebesgu3integralsettingareobtained.Thesesharpenearlierresults.

简介：TheprimarypurposeofthispaperistopresenttheVolterraintegralequationofthetwo-variableHermitematrixpolynomials.Moreover,anewrepresentationofthesematrixpolynomialsareestablishedhere.

简介：WeconsiderthemultidimensionalabstractlinearintegralequationofVolterratypex（t）+（*）∫Rtα（s)x(s)ds=f(t),t∈R，（1）asthelimitofdiscreteStieltjes-typesystemsandweproveresultsontheexistenceofcontinuoussolutions.Thefunctionsx,αandfareBauachspace-valueddefinedonacompactintervalRofR^nRtisasubintervalofRdependingont∈Rand(*)fdenoteseithertheBochner-LebesgueintegralortheHenstockintegral.Theresultspresentedheregeneralizethosein[1]andareinthespiritof[3].Asaconsequenceofourapproach,itispossibletostudythepropertiesof(1)bytransferringthepropertiesofthediscretesystems,TheHenstockintegralsettingenablesustoconsiderhighlyoscillatingfunctions.

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简介：UsingafixedpointtheoremofKrasnosel'skiitype,thisarticleprovestheexistenceofasymptoticallystablesolutionsforaVolterra-Hammersteinintegralequationintwovariables.

简介：ThediscretedynamicsforcompetitionpopulationsofLotka-VolterratypemodeledasN1(t+1)=N1(t)exp[r1(1-N1-b12N2)],N2(t+1)=N2(t)exp[r2(1-N2-b21N1)]isconsideredinthepaper.Inthecaseofnon-persistencetheattractivebehaviorofmodelhasbeendiscussed.Especially,therearetwoattractivesetswhenbij>1,andtheattractivebehaviorsaremorecomplicatedthanthatofthecorrespondingcontinuousmodel.Theattractedregionsaregiven.Weprovethatthemodelisalsopersistentinthedegeneratecaseofbij=1.Inthepersistencecaseofbij<1,theexistenceanduniquenessfortwo-periodpointsofthemodelarestudiedatr1=r2.Theconditionforthemulti-pairoftwo-periodpointsisindicatedandtheirinfluencesonpopulationdynamicalbehaviorsareshown.

简介：ThispaperdealswiththeuniquenessandexistenceofperiodicsolutionsofneutralVolterraintegrodifferentialequations(1)and(2).Somenewuniqueexistencecriteriaareobtained.

简介：ThepurposeofthispaperistostudythesuperconvergencepropertiesofRitz-Volterraprojection.ThroughconstructionanewtypeofGreenfunctionandmakinguseofitspropertiesandtheprincipleofduality,thepaperprovesthattheRitz-Volterraprojectiondefinedonr-1orderfiniteelementspacesofLagrangetypeinoneandtwospacevariablecasespossessesO(h2r~2)orderandO(h4+1|Inh|)ordernodalsuperconvergence,respectively,andthesametypeofsuperconver-genceresultsaredemonstratedforthesemidiscretefinitedementapproximatesolutionsofSoboleve-quations.

简介：§1.IntroductionItisknownthatthefollowingCauchyproblemforaparabolicpartialdifferentialequation(wherethevaluesattherightboundary,u.(1,t)=v(t)areunknownandsoughtfor)isill-posed:thesolution(v)doesnotdependcontinuouslyonthedata(g).Inordertotreattheill-posednessanddevelopthenumericalmethod,onereformulatestheproblemasaVolterraintegralequationofthefirstkindwishaconvolutiontypekernel(seeSneddon[1],CarslawandJaeger[2])

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简介：Inthispaper,aLotka-Volterracooperationsystemwithsinglefeedbackcontrolisproposedandstudied.Weinvestigatethelocalstabilityandtheglobalstabilityofthesystem.Ourstudyshowsthatwithsuitablerestrictiononthecoefficientsofthefeedbackcontrolvariable,thesystemcanstillremaingloballystableorbecomeextinct,whichshowsthatthefeedbackcontrolvariableplaysaveryimportantroleinthedynamicsbehaviorsofthesystem.

简介：ThepurposeofthispaperistostudythestabilityandapproximationpropertiesofRitz-Volterraprojection.ThroughconstructinganewtypeofGreenfunctionsandmakinguseofvariouspropertiesandestimatesrelatedwiththefunctions,weprovethattheRitz-Volterraprojectiondefinedonthefinite-dimensionalsubspaceS_hofH_o~1possessestheW_p~1-stabilityandtheoptimalapproximationpropertiesinW_p~1andL_pfor2≤p≤∞.Ourresults,inthispaper,canbeappliedtothefiniteelementapproximationsformanyevolutionequationssuchasparabolicandhyperbolicintegrodifferentialequations,Sobolevequationsandvisco-elasticity,etc.

简介：Inthispaper,weproposeaLotka-Volterraprey-predatorsystemwithdiscretedelaysandfeedbackcontrol.Firstly,weshowthatsolutionofthesystemisbounded.Secondly,weobtainsufficientconditionfortheglobalstabilityoftheuniquepositiveequilibriumtothesystem.

简介：Inthispaper,wepresentastabilityanalysisofaLotka-VolterracommensalsymbiosismodelsubjecttoAlleeeffectontheunaffectedpopulationwhichoccursatlowpopulationdensity.ByanalyzingtheJacobianmatrixaboutthepositiveequilibrium,weshowthatthepositiveequilibriumislocallyasymptoticallystable.Byapplyingthedifferentialinequalitytheory,weshowthatthesystemispermanent,consequently,theboundaryequilibriaofthesystemisunstable.Finally,byusingtheDulaccriterion,weshowthatthepositiveequilibriumisgloballystable.AlthoughAlleeeffecthasnoinfluenceonthefinaldensitiesofthepredatorandpreyspecies,numericsimulationsshowthatthesystemsubjecttoanAlleeeffecttakesmuchlongertimetoreachitsstablesteady-statesolution,inthissensethatAlleeeffecthasunstableeffectonthesystem,however,suchaneffectiscontrollable.Suchanfindingisgreatlydifferenttothatofthepredator-preymodel.

简介：本文对积分算子Ｉ_α作了进一步的讨论，并利用它，得到了常系数Ｖｏｌｔｅｒｒａ弱奇异积－微分方程的一种算子解法．

简介：本文引入契贝晓夫多项式作为基函数,利用Galerkin方法研究了一类Fredholm-Volterra积分方程的数值解,并进行了数值模拟.结果表明,该方法可行且有效.

简介：利用迭合度理论的连续定理,讨论了一类中立型系统的正周期解的存在性.得到了正周期解存在的一些充分条件.

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简介：本文给出了Volterra积分微分方程的零解关于部分变元的稳定性定义,并建立了几个判定定理。

简介：利用迭合度理论的连续定理,讨论了一类中立型系统的正周期解的存在性.得到了正周期解存在的一些充分条件.