UPPER AND LOWER SOLUTIONS METHODS FOR EXISTENCE OF PERIODIC SOLUTIONS OF DUFFING EQUATION

1.IntroductionandNotationsInthispapertwestudytheexistenceofsolutionstothefollowingperiodicboundaryvalueproblemforthesecondorderDuffingequationwheresisarealparameter,g:[0,TIxR~RisaCarath6odoryfunctionandkER\{0}.Werecall(forexample,see[1])thatg:[0,TIxR~RiscalledaCarath6odoryfunctionifg(.,x)ismeasurableforallxERandg(t,.)iscontinuousfora.e.tE[0,TI.Theexistenceproblemfor(1.1)--(1.2)byusingtheupperandlowersolutionsmethodhasbeenstudiedbyFabryetal.in[2]foramoregeneralcasewhereacontinuousdampin…     

EXISTENCE OF NONTRIVIAL SOLUTIONS FOR CRITICAL SEMILINEAR BIHARMONIC EQUATIONS

ＥＸＩＳＴＥＮＣＥＯＦＮＯＮＴＲＩＶＩＡＬＳＯＬＵＴＩＯＮＳＦＯＲＣＲＩＴＩＣＡＬＳＥＭＩＬＩＮＥＡＲＢＩＨＡＲＭＯＮＩＣＥＱＵＡＴＩＯＮＳ￥ＧＵＹｏｎｇｇｅｎｇ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅ...     

FINITE DIMENSIONAL BEHAVIOR FOR THE DISSIPATIVE GENERALIZED SYMMETRIC REGULARIZED LONG WAVE EQUATIONS

This paper deals with the asymptotic behaviour of solutions for the generalized symmetric regularized long wave equations with dissipation term. We first show the existence of global weak attractors for the periodic initial value problem of this equations in H2 x H1. And then by an energy equation and an idea of Ghidaglia and Guo, we conclude that the global weak attractor is actually the global strong attractor for S(t) in H2(2) x H1(M).The finite dimensionality of the global attractor is also established.     

EXISTENCE, MULTIPLICITY AND BIFURCATION FOR CRITICAL POLYHARMONIC EQUATIONS

1.IntroductionLetfibeaboundeddomaininR"withn23andoffbesufficientlysmooth.WeareconcernedwiththesemilinearellipticequationofhigherordersinvolvingcriticalSobolevexpelwhere,andthroughoutthispaper,gistheunitoutwardnormaltooff,25Zm相似文献   

一类对称双势阱Duffing系统周期解的衍生与演化

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QUENCHING PHENOMENA FOR SYSTEMS OF SEMILINEAR PARABOLIC EQUATIONS I

1.IntroductionConsiderthefollowinginitial-boundaryvalueproblemforthesystemsofsemilinearparabolicequationsWhereG.~(--a,a)x(0,Ta),r.~({--a,a}x[0,Ta))U([--a,a]x{0}),andf(z)andg(z)satisfy(FGI)f(z):(--co,ba)-R ,g(z):(--co,bl)-R ,f(0)>0,andg(0)>0;(FG2)i(z)andg(…     

EXISTENCE AND NONEXISTENCE OF POSITIVE RADIAL SOLUTIONS FOR A CLASS OF SEMILINEAR ELLIPTIC SYSTEMS

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THE PERIODIC HOLLING Ⅱ PREDATOR-PREY MODEL WITH IMPULSIVE EFFECT

In this paper, a periodic Holling II predator-prey model with impulsive effect is investigated. By applying the Floquet theory of linear periodic impulsive equation, some sufficient conditions are obtained for the linear stability and instability of trivial and semi-trivial periodic solutions. Moreover, we use standard bifurcation theory to show the existence of coexistence states which arise near the semi-trivial periodic solution. As an application, we also examine some special case of the system to confirm our main results.     

SOLITON AND ELLIPTICAL PERIODIC SOLUTIONS TO THE MODIFIED NONLINEAR SCHRODINGER EQUATION

1.IntroductionAsiswellknown,theNLSE.02 ac Iql:q=0(1)'N Zap Iql:q=0(1)describesthepropagationofpicosecondOPticalpulseinamonomodeOPticalfiber,whereq(',T)istocomplexpulse,'represelltsthedistancealongthedirectionofpropagation,Trepresentsthetimeinthegroupvelocityframeandrs=11.TheNLSEhasbrightsolitonsolutionwhend==1,anddarksolitonsolutionwhena=11.Inthisnotewehaveobtainedthedarksolitonsolutionwhena~1.However,recentworkshaveshownthattheNLSEisnotsufficieDttodescribethepropagationoffemtosecond…     

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基于可分任务理论,研究大规模计算中的应用调度问题。利用线性规划得到了周期性的多趟调度算法的数学模型。针对同构计算平台进行参数优化,得到如下解析结果:(1)在处理机选定的情况下得到优化的调度趟数;(2)在趟数给定的情况下得到优化的处理机选择方法;(3)对于给定的任务,得到优化的处理机选择方法和相应的趟数。仿真结果表明所得结果的正确性。     

A HOMOCLINIC ORBIT FOR LAGRANGIAN SYSTEMS

ＡＨＯＭＯＣＬＩＮＩＣＯＲＢＩＴＦＯＲＬＡＧＲＡＮＧＩＡＮＳＹＳＴＥＭＳＷＵＳｈａｏｐｉｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＺｈｅｊｉａｎｇＵｎｉｖｅｒｓｉｔｙ，Ｈａｎｇｚｈｏｕ３１００２７，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ：Ｗｅｐｒｏ...     

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Existence of Positive Periodic Solutions of Competitor-Competitor-Mutualist Lotka-Volterra Systems with Infinite Delays

In this paper,the authors primarily explore a delayed competitor-competitor-mutualist Lotka-Volterra model,which is a system of differential equation with infinite integral.The authors first study the existence of positive periodic solutions of the model by using the Krasnoselskii’s fixed point theorem,and then present an example to illustrate the main results.     

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In this paper, we study the existence and global asymptotic stability of positive periodic solutions of a delayed periodic predator-prey system with Hoffing Ⅱ type functional response. By use of the continuation theorem of coincidence degree theory and the method of Lyapunov function, some sufficient conditions are obtained.     

飞机旋转叶片回波频谱特征分析

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THE GENERALIZED SOLUTIONS OF PBVP FOR INTEGRO-DIFFERENTIAL EQUATIONS

ＴＨＥＧＥＮＥＲＡＬＩＺＥＤＳＯＬＵＴＩＯＮＳＯＦＰＢＶＰＦＯＲＩＮＴＥＧＲＯ－ＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＺＨＵＡＮＧＷａｎ；ＣＨＥＮＹｕｂｏ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｈａｎｄｏｎｇＮｏｒｍａｌＵｎｉｖｅｒｓ...     

Existence and Global Exponential Stability of Pseudo Almost Periodic Solutions of a General Delayed BAM Neural Networks

This paper studies a class of general BAM neural networks with multiple delays. Employing the exponential dichotomy theory and fixed point method, together with constructing suitable Lyapunov functionals, easily verifiable delay-independent criteria are established to ensure the existence and global exponential stability of pseudo almost periodic solutions, which not only generalize but also complement some existing ones. These theoretical results are also supported with numerical simulations.     

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Hopf bifurcation analysis in a 4D-hyperchaotic system

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In this paper, a delayed ratio-dependent Holling-III predator-prey system with stagestructured and impulsive stocking on prey and continuous harvesting on predator is considered. The authors obtain sufficient conditions of the global attractivity of predator-extinction periodic solution and the permanence of the system. These results show that the behavior of impulsive stocking on prey plays an important role for the permanence of the system. The authors also prove that all solutions of the system are uniformly ultimately bounded. The results show that the biological resource management is effective and reliable.