一个Duffing方程的调和解和次调和解

本文证明了Duffing方程x+arctan x=p(t)的调和解和无穷多的次调和解的存在 性,其中周期的2π连续函数p(t)满足|p(t)|<π/2,(?)t∈R.     

二阶超线性差分方程周期解与次调和解的存在性

应用临界点理论, 为研究差分方程周期解与次调和解的存在性和多重性提供了一种新方法. 对二阶差分方程 D²x_n-1+f (n, x_n)=0, 当f(t, z)在0点及无穷远点为超线性增长时, 上述问题得到某些新结果.     

一类一阶Hamilton系统的次调和解

运用临界点理论中的极小极大方法得到一类一阶Hamilton系统的次调和解的存在性定理.     

一类局部非二次Hamilton系统的次调和解的存在性

运用极小极大方法得到一类局部非二次的Hamilton系统的次调和解的存在性定理.     

一类三维系统的次调和解与不变环面的分支

讨论一类三维自治系统的闭轨在周期扰动下的分支问题.利用Poincare映射与积分流形定理,得到扰动系统存在次调和解和不变环面的条件,以及次调和解的鞍结点分支.     

一类次线性非自治二阶系统的多重周期解

利用广义鞍点定理研究非自治二阶系统周期解的存在性.在具有部分周期位势和次线性增长非线性项时,给出了多重周期解存在的充分条件,所得结论推广了已知结果.     

高维Lienard型方程的调和解

本文运用重合度理论，在阻尼可负的条件下，得到Ｌｉｅｎａｒｄ型系统存在调和解的若干新判据。     

调和解存在的一个充分条件

给出具有两个实自变数的未知函数的线性偏微分方程(组)调和函数解存在的一个充分条件，及在此条件下方程(组)调和函数解的简化求法。     

双曲极限环在周期扰动下次调和解的分支

研究了一给定平面自治系统的双曲极限环在周期扰动下m阶次调和解的分支问题,用Poincar啨映射,通过变尺度方法,获得了判别m阶次调和解的存在条件,最后给出了一个实例。     

EXISTENCE OF POSITIVE SOLUTIONS TO SINGULAR SUBLINEAR SEMIPOSITONE NEUMANN BOUNDARY VALUE PROBLEM

The existence of positive solutions to a singular sublinear semipositone Neumann boundary value problem is considered. In this paper,the nonlinearity term is not necessary to be bounded from below and the function q(t) is allowed to be singular at t = 0 and t = 1.     

BOUNDEDNESS OF SOLUTIONS FOR SUPERLINEAR REVERSIBLE SYSTEMS

51. IntroductionThe boundedness problem of solutions of the following nonlinear scalar differelltial equa-nons of second order..x f(x, t)ic g(x, t) = 0 (1'1)has been widely investigated by many authors since the 1940's, where f(x, t 1) = j(x, t),g(x, t 1) = g(x, t).When j(x, t) = 0, Equation (1.1) is a conservative system and takes the following form..x g(x, t) ~ 0. (1'2)The first contribution of the boundedness of all the solutions of Equation (1.2) is due toMorrislll, whO proved …     

PERIODIC SOLUTIONS OF ASYMPTOTICALLY LINEA RHAMILTONIAN SYSTEMS

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

EXISTENCE OF POSITIVE ENTIRE SOLUTIONS FOR QUASILINEAR ELLIPTIC SYSTEMS

In this paper, the existence of positive solutions for a class of quasilinear elliptic differential equation systems are established by Schauder-TychonofF fixed point theorem.     

STABILITY OF SUBHARMONIC SOLUTIONS OF FIRST-ORDER HAMILTONIAN SYSTEMS WITH ANISOTROPIC GROWTH

Using the dual Morse index theory, we study the stability of subharmonic solutions of first-order autonomous Hamiltonian systems with anisotropic growth, that is, we obtain a sequence of elliptic subharmonic solutions(that is, all its Floquet multipliers lying on the unit circle on the complex plane C).     

THE EXISTENCE OF HOMOCLINIC ORBITS FOR HAMILTONIAN SYSTEMS WITH THE POTENTIALS CHANGING SIGN

§1.ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＭａｉｎＲｅｓｕｌｔｓ　　ＷｅｃｏｎｓｉｄｅｒｔｈｅＨａｍｉｌｔｏｎｉａｎｓｙｓｔｅｍｓ¨ｑ-Ｌ(ｔ)ｑ Ｖ′(ｔ,ｑ)=0,(ＨＳ)ｗｈｅｒｅ(ｔ,ｑ)∈Ｒ×ＲＮ,¨ｑ=ｄ2ｄｔ2ｑ,Ｖ′(ｔ,ｑ)ｄｅｎｏｔｅｓｔｈｅｇｒａｄｉｅｎｔｏｆＶ(ｔ,ｑ)ｗｉｔｈｒｅｓｐｅｃｔｔｏｑ,ａｎｄｔｈｅｓｙｍｍｅｔｒｉｃｍａｔｒｉｘＬ(ｔ)ｉｓａｓｓｕｍｅｄｔｏｓａｔｉｓｆｙ:(Ｌ)Ｌ(ｔ)∈Ｃ(Ｒ,ＲＮ2)ａｎｄｔｈｅｒｅｅｘｉｓｔｓλ>0ｓｕｃｈｔｈａｔＬ(ｔ)ｘ·ｘλ｜ｘ｜2,(ｔ,ｘ)∈Ｒ×ＲＮ.Ｗｅａｓｓｕｍ…     

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.     

POSITIVE PERIODIC SOLUTIONS OF PREDATOR-PREY SYSTEMS WITH INFINITE DELAY

1.IntroductionPredator-preysystemsareonekindsofecologicalsystems,theyhaveattractedmuchattentioninrecentyears.Butuptonow,mostoftheknownresultsareconcernedwithsystemswithouttimedelayorwithfinitedelay[1-6].Infinitedelaywillcausemuchmoretroublethanfinitedelaydoes,andcorrespondingresultsaremuchfewe.[7-9].Inthispaper,usingthepersistenceconclusionsof[9],weintroduceanewargument;withoututilizingcomplicatedphasespacetheory,changingtheperiodicsolutionproblemofinfinitedelaytotheoneoffinitedelay,newandbrie…     

POSITIVE PERIODIC SOLUTIONS OF THE FIRST- ORDER SINGULAR DISCRETE SYSTEMS

In this paper, we study two kinds of first-order singular discrete systems. By the fixed point index theory, we investigate the existence and multiplicity of positive periodic solutions of the systems.     

EXISTENCE OF MULTIPLE PERIODIC SOLUTIONS TO A SECOND-ORDER NONLINEAR DIFFERENCE SYSTEM

In this paper, by the critical point theory, a sufficient condition for the existence of multiple periodic solutions to a nonlinear second order difference system is obtained. An illustrative example is given. Our results improve and generalize some known ones.