学科分类
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257 个结果
  • 简介:TheKurzweil-HenstockintegralformalismisappliedtoestablishtheexistenceofsolutionstothelinearintegralequationsofVolterra-typewherethefunctionsareBanach-spacevalued.SpecialtheoremsonexistenceofsolutionsconcerningtheLebesgu3integralsettingareobtained.Thesesharpenearlierresults.

  • 标签: LINEAR VOLTERRA INTEGRAL EQUATIONS Kurzweil-Henstock INTEGRALS
  • 简介:TheprimarypurposeofthispaperistopresenttheVolterraintegralequationofthetwo-variableHermitematrixpolynomials.Moreover,anewrepresentationofthesematrixpolynomialsareestablishedhere.

  • 标签: VOLTERRA积分方程 矩阵多项式 埃尔米特
  • 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.

  • 标签: 线性电压积分方程 连续解 存在性 巴拿赫空间
  • 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.

  • 标签: 离散动力学 LOTKA-VOLTERRA模型 存在性 唯一性
  • 简介:ThispaperdealswiththeuniquenessandexistenceofperiodicsolutionsofneutralVolterraintegrodifferentialequations(1)and(2).Somenewuniqueexistencecriteriaareobtained.

  • 标签: UNIQUENESS NEUTRAL deals ARGUMENT LEMMA 扫刀
  • 简介:ThepurposeofthispaperistostudythesuperconvergencepropertiesofRitz-Volterraprojection.ThroughconstructionanewtypeofGreenfunctionandmakinguseofitspropertiesandtheprincipleofduality,thepaperprovesthattheRitz-Volterraprojectiondefinedonr-1orderfiniteelementspacesofLagrangetypeinoneandtwospacevariablecasespossessesO(h2r~2)orderandO(h4+1|Inh|)ordernodalsuperconvergence,respectively,andthesametypeofsuperconver-genceresultsaredemonstratedforthesemidiscretefinitedementapproximatesolutionsofSoboleve-quations.

  • 标签: SUPERCONVERGENCE Ritz-Volterra PROJECTION FINITE element SOBOLEV
  • 简介:§1.IntroductionItisknownthatthefollowingCauchyproblemforaparabolicpartialdifferentialequation(wherethevaluesattherightboundary,u.(1,t)=v(t)areunknownandsoughtfor)isill-posed:thesolution(v)doesnotdependcontinuouslyonthedata(g).Inordertotreattheill-posednessanddevelopthenumericalmethod,onereformulatestheproblemasaVolterraintegralequationofthefirstkindwishaconvolutiontypekernel(seeSneddon[1],CarslawandJaeger[2])

  • 标签: FIRST posed KERNEL CONVOLUTION sought PARABOLIC
  • 简介:Inthispaper,aLotka-Volterracooperationsystemwithsinglefeedbackcontrolisproposedandstudied.Weinvestigatethelocalstabilityandtheglobalstabilityofthesystem.Ourstudyshowsthatwithsuitablerestrictiononthecoefficientsofthefeedbackcontrolvariable,thesystemcanstillremaingloballystableorbecomeextinct,whichshowsthatthefeedbackcontrolvariableplaysaveryimportantroleinthedynamicsbehaviorsofthesystem.

  • 标签: 数学分析 数学理论 应用数学 函数
  • 简介:ThepurposeofthispaperistostudythestabilityandapproximationpropertiesofRitz-Volterraprojection.ThroughconstructinganewtypeofGreenfunctionsandmakinguseofvariouspropertiesandestimatesrelatedwiththefunctions,weprovethattheRitz-Volterraprojectiondefinedonthefinite-dimensionalsubspaceS_hofH_o~1possessestheW_p~1-stabilityandtheoptimalapproximationpropertiesinW_p~1andL_pfor2≤p≤∞.Ourresults,inthispaper,canbeappliedtothefiniteelementapproximationsformanyevolutionequationssuchasparabolicandhyperbolicintegrodifferentialequations,Sobolevequationsandvisco-elasticity,etc.

  • 标签: Ritz-Volterra PROJECTION STABILITY and approximation.
  • 简介:Inthispaper,weproposeaLotka-Volterraprey-predatorsystemwithdiscretedelaysandfeedbackcontrol.Firstly,weshowthatsolutionofthesystemisbounded.Secondly,weobtainsufficientconditionfortheglobalstabilityoftheuniquepositiveequilibriumtothesystem.

  • 标签: LOTKA-VOLTERRA PREY-PREDATOR SYSTEM FEEDBACK CONTROL GLOBALSTABILITY
  • 简介:用变分方法研究非自治Lagrange系统周期解的问题转化为研究Lagrange作用泛函的临界点问题.对Lagrange系统,人们用变分方法已经获得了一系列可解性条件,但是除在超二次条件下,Lagrange作用泛函都是下方有界的.这里的目的是给出Lagrange作用泛函无界的Lagrange系统周期解的其它可解性条件.这时的主要困难是对应的Lagrange作用泛函不再是下方有界的.这里用临界点理论中的鞍点定理得到了Lagrange系统周期解的存在性.

  • 标签: 非自治Lagrange系统 周期解 变分法 作用泛函 临界点 鞍点定理
  • 简介:Inthispaper,wepresentastabilityanalysisofaLotka-VolterracommensalsymbiosismodelsubjecttoAlleeeffectontheunaffectedpopulationwhichoccursatlowpopulationdensity.ByanalyzingtheJacobianmatrixaboutthepositiveequilibrium,weshowthatthepositiveequilibriumislocallyasymptoticallystable.Byapplyingthedifferentialinequalitytheory,weshowthatthesystemispermanent,consequently,theboundaryequilibriaofthesystemisunstable.Finally,byusingtheDulaccriterion,weshowthatthepositiveequilibriumisgloballystable.AlthoughAlleeeffecthasnoinfluenceonthefinaldensitiesofthepredatorandpreyspecies,numericsimulationsshowthatthesystemsubjecttoanAlleeeffecttakesmuchlongertimetoreachitsstablesteady-statesolution,inthissensethatAlleeeffecthasunstableeffectonthesystem,however,suchaneffectiscontrollable.Suchanfindingisgreatlydifferenttothatofthepredator-preymodel.

  • 标签: LOTKA-VOLTERRA COMMENSAL SYMBIOSIS MODEL Allee effect
  • 简介:研究了一类具无穷时滞的中立型周期微分系统周期解的存在性问题.利用指数型二分性及Krasnoselskii不动点定理,建立了保证该系统周期解的存在性的充分条件.所得结果推广了文[1—7]的有关结果.

  • 标签: 中立型周期微分系统 周期解 存在性
  • 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.

  • 标签: 积分算子 积-微分方程 解法