具分布时滞的一类 Logistic方程的周期正解(英文)Positive periodic solutions of a logisticequation with distributed delays
卢玲红,李永昆
摘要(Abstract)：
利用重合度定理 ,建立了下面具分布时滞的 L ogistic方程x′( t) =x( t) ∑ni=1ri( t) 1 - 1K( t) ∫t-∞x( s) ds Ri( t,s)正周期存在的充分条件 .其中 ri( t) ,K( t)和 Ri( t,s)是以ω >0为周期的正周期函数
关键词(KeyWords)： 周期正解;Logistic方程;分布时滞;重合度定理
基金项目(Foundation): 国家自然科学基金 ( 10 3 610 0 6);; 云南省自然科学基金 ( 2 0 0 3 A0 0 0 1M)资助项目
作者(Author): 卢玲红,李永昆
参考文献(References)：
- [1] GopalsamyK.Stability andOscillatikon inDelayDifferentialEquations ofPopulationDynamics[M].KluwerAcademicPublishers.Dordrecht,Boston,L ondon.1992.
- [2] BerezanskyL,BravermanE.Oscillation properties of a logistic equation with distributed delay[J].Non-linearAnalysis:RealWorldApplications,2003,4(1):1～19.
- [3] GainesR E,MawhinJL.CoincidenceDegree andNonlinearDifferentialEquaitons[M].Springer-Ver-lag,Berlin,1977.
- [4] BerezanskyaL,BravermanbE.On oscillation of a logistic equation with several delays[J].Journal ofcomputational andAppliedMathematics,2000,113(1-2):255～265
- [5] KowalczykR,Fory s′U.QualitativeAnalysis on theInitialValueProblem to theL ogisticEquation withDelay[J].Mathematical andComputerModelling,2002,35(1-2):1～13.
- [6] FanG,L iY.Existence of positive periodic solutions for a periodic logistic equation[J].AppliedMathe-matics andComputation,2003,139(2-3):311～321.
- [7] YuanR.On the logistic delay differential equations with piecewise constant argument and quasi- periodictime dependence[J].J.Math.Anal.Appl.,2002,274(1):124～133