MULTIPLICITY OF POSITIVE PERIODIC SOLUTIONS TO SECOND ORDER SINGULAR DIFFERENTIAL SYSTEMS

In this article, the author is devoted to establish the multiplicity of positive periodic solutions to second-order singular differential systems. It isproved that such a problem has at least two positive solutions under our reasonable conditions. The proof relies on a nonlinear alternative of Leray--Schauder type and Krasnoselskii fixed point theorem in cones.     

THE STABILITY OF THE PERIODIC SOLUTIONS OF SECOND ORDER HAMILTONIAN SYSTEMS

51.IntroductionandMainResultsInthispaper,weconsiderthestabilityoftheperiodicsolutionsofthefollowingsecondorderHamiltoniansystemswherenisapositiveillteger.V:Rxac-RisafUnctionandforT>0itisT-periodicforthevariablet.VJdenotesitsgradientwithrespecttox.Wenowstatethemainresultsofthispaper.Forthesuperquadraticcase)wehavethefollowingtwotheoremsTheorem1.1.SmposeVsatiSfiesthefollowingconditions:(VI)VEC'(RxR",R)andV(t T,x)=V(t,x),V(t,x)ERxR".(V2)ThereexistconstantSp>2andco>0suchthat0相似文献   

MULTIPLICITY OF POSITIVE PERIODIC SOLUTIONS TO SECOND ORDER SINGULAR DIFFERENTIAL SYSTEMS

In this article, the author is devoted to establish the multiplicity of positive periodic solutions to second-order singular differential systems. It is proved that such a problem has at least two positive solutions under our reasonable conditions. The proof relies on a nonlinear alternative of Leray- Schauder type and Krasnoselskii fixed point theorem in cones.     

一类带阻尼项的次二次二阶Hamilton系统的周期解

本文研究了一类带阻尼项的二阶Hamilton系统周期解的存在性问题.利用鞍点定理,在新的次二次条件下,获得了一个新的存在性结果,推广并改进了已有文献的相关存在性结论.     

一类四阶离散哈密顿系统周期解的存在性

本文研究了一类四阶离散哈密顿系统周期解的存在性问题.利用临界点理论中的极大极小方法,通过引入两个不同的控制函数,得到了新的可解性条件,并且利用这些条件得到了新的存在性结果.     

MULTIPLE SOLUTIONS FOR NONAUTONOMOUS SECOND ORDER PERIODIC SYSTEMS

We study nonautonomonus second order periodic systems with a nonslnooth potential. Using the nonsmooth critical theory, we establish the existence of at least two nontrivial solutions. Our framework incorporates large classes of both subquadratic and superquadratic potentials at infinity.     

POSITIVE SOLUTIONS TO SINGULAR SECOND ORDER PERIODIC BOUNDARY VALUE PROBLEM WITH SIGN-CHANGING NONLINEARITIES

This paper deals with the existence of positive solutions to the singular secondorder periodic boundary value problem. We obtain the existence results of positive solutions by the fixed point index theory. The results obtained extend and complement some known results.     

POSITIVE SOLUTIONS OF PERIODIC BOUNDARY VALUE PROBLEM FOR SECOND ORDER DIFFERENTIAL SYSTEMS

In this paper, by utilizing a fixed point theorem on cone in Banach space, the author disscusses the periodic boundary value problem of second order differential systems. Some results on the existence of positive solutions are derived.     

跳跃非线性项依赖于导数的二阶微分方程周期解的存在性

本文研究二阶微分方程χ"+aχ+-bχ-+f(χ)g(χ'=p(t)周期解的存在性,这里χ+=max{χ,0},χ-=max{-χ,0},a,6是正常数并且点(a,b)位于某一条Fucik谱曲线上.当g(χ)的极限lim.g(χ)=g(+∞),lim g(χ)=g(-∞)和f(χ)的极限lim,g(χ)=f(+∞),lim f(χ)=f(-∞)都存在且有限时,给出了此方程存在周期解的充分条件.     

跳跃非线性项依赖于导数的二阶微分方程周期解的存在性

本文研究二阶微分方程x"+ax+-bx-+f(x)g(x')=p(t)周期解的存在性,这里x+=max{x,0},x-=max{-x,0},a,b是正常数并且点(a,b)位于某一条Fucik谱曲线上.当g(x)的极限limx→∞(x)=g(+∞),limx→∞g(x)=g(-∞)和f(x)的极限limx→∞f(z)=f(+∞),limx→∞f(z)=f(-∞)都存在且有限时,给出了此方程存在周期解的充分条件.     

PERIODIC SOLUTIONS OF ASYMPTOTICALLY LINEA RHAMILTONIAN SYSTEMS

ＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＯＦＡＳＹＭＰＴＯＴＩＣＡＬＬＹＬＩＮＥＡＲＨＡＭＩＬＴＯＮＩＡＮＳＹＳＴＥＭＳＦｅｉＧｕｉｈｕａＱｉｕＱｉｎｇｊｉｕＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＤｅｃｅｍｂｅｒ５，１９９４．ＲｅｖｉｓｅｄＳｅｐｔｅ...     

渐近线性 Hamiltonian 系统的周期解

一、引言和定理的陈述设 H=H(t,z)∈C~1(R×R~(2N)),N≥2.考虑下面的 Hamiltonian 系统Z=JH′(t,z),(t,z)∈R×R~(2N),(1.1)其中 H′表示 H 关于 z 变量的梯度,J是R~(2N)中的标准辛结构,J=■假定 Hamiltonian 函数 H 周期地依赖于时间 t,即H(t T,z)=H(t,z),这里 T>0是周期.本文欲寻求系统(1.1)的 T-周期解.文中限于讨论满足下述条件的     

一类具有无穷多个周期解的二阶偏微分方程

本文首先给出了一类具有无穷多个周期解的无阻尼二阶线性偏微分方程所描述的系统。同时讨论了一类无阻尼非线性二阶偏微分方程存在多个周期解的情况，最后给出了一个判断有阻尼二阶偏微分系统存在周期解的方法。     

二阶中立型方程的周期解

本文改进了文[1]的主要结果,即将文[1]定理1中的条件|c|<1/2,改为|c|≠1,从而文[1]的其它定理可相应进行改进。     

非自治 Hamilton 系统多重周期解的存在性

一、引言和主要结果在临界点理论中,我们知道如果具有变分结构的方程含有某种对称性,则对应的泛函在相应的群(例如 Z_2或 S~1)作用下是不变的.这种泛函常常具有多重临界点甚至无穷多个临界点,对应的方程同时具有多重解.令人感兴趣的问题是如果这种对称性被扰动,在什么条件下多重解的性质仍能保持?这类问题对于半线性椭圆型方程,半线性波动方程以及Hamilton 系统已有了若干重要的结果,也已提出了许多保证无穷多解存在性的充分性条件.但这些结果都只考虑具有某种对称性的主要非线性项是超线性时的情形,而对称扰动项或是自由项或其增长阶低于对称项的增长阶.一个自然的问题是能否提出另外一类保证无穷多解存在性的充分条件.例如对称项的增长阶低于扰动项的增长阶?本文将部     

HOMOCLINIC ORBITS FOR A CLASS OF THE SECOND ORDER HAMILTONIAN SYSTEMS

The existence of homoclinic orbits is obtained by the variational approach for a class of second order Hamiltonian systems q(t)+▽V(t,q(t))=0,where V(t,x)=-K(t,x)+W(t,x),K(t,x) is neither a quadratic form in x nor periodic in t and W(t,x) is superquadratic in x.     

不满足Gordon-强力条件的奇异二阶周期Hamilton系统同宿轨道的存在性

考虑奇异的二阶周期 Hamilton 系统这里q=(q_1,q_2,…,q_n)∈R~n,n>2,V(t,q):R×R~n\{e}→R 是一个奇异的位势函数,e≠0.当V(t,q)具有唯一最大值,但不满足 Gordon- 强力条件时,我们证明了(HS)至少具有一条非平凡的同宿轨道。     

二阶多时滞非线性微分方程的周期解

研究二阶系数非线性多时滞微分方程ω周期解的存在性，得到了ω周期解存在的充分条件。     

二阶非线性差分方程多重周期解的存在性

本文研究了一类带参数非自治的二阶非线性差分方程多重周期解的存在性问题.利用Morse理论,建立了此类方程多重周期解的存在性准则.