On the Nonexistence of Laurent Polynomial First Integrals for General Semi－quasihomogeneous Systems

An autonomous system of ODFs which admitting a quasi-homogeneous group of symmetries is called a quasihomogeneous one.     

On the Nonexistence of Laurent Polynomial First Integrals for General Nonlinear Systems

The integrability of a system of ODEs 圣=/(x1is defined as the existence of a sufficiently rich set of first integrals such that its solutions canbe expressed by these integrals.Here,a single-valued function西(。)is called a first integralof the system(1)if it is constant along any solution curve of the system(1).If≯(z)isdifferentiable,then this definition can be written as the condition (筹川瑚=0.The singularity analysis has been proved to be a successful tool for finding integrable systems…     

随机泛函微分方程解的稳定性

通过定义随机Lyapunov过程, 研究随机泛函微分方程的零解在均值意义下的稳定性.     

非线性系统有理首次积分的不存在性和部分存在性

该文的目的是给出一般非线性系统存在和部分存在有理首次积分的判别准则. 作者给出系统存在有理首次积分的必要条件, 在此基础上进一步给出系统不存在其它有理首次积分(在函数独立的意义下)的判定准则.     

催化反应中的一类奇摄动边值问题

§1. Introduction We are concered with the singularly perturbed boundary value problemε2y″=y3,(1)y(0)=1, y(1)=2,(2)where ε＞0 is a positive small parameter. This problem arises as models for certain catalytic reactions in chemical engineering. The study of that problem has been paid much attention for the boundary layers of the problem exihibit the behavior of nonexponential decay. There have been some works on this subject ［1］-［4］. In particular, Howes and Chang［1］ gave an accurate…     

泛函微分包含问题周期解的存在性

用Horn渐近不动点定理, 给出具非凸右端函数的泛函微分包含问题周期解存在性的 一般性结果.     

具非凸右端项泛函微分包含的周期解

In this paper we present a general existence result of periodic solutions for functional differential inclusions with nonconvex right hand sides, by using the asymptotic fixed point theory. In our result, the uniform boundedness and ultimate boundedness are only assumed to the solutions with bounded initial functions. On the other hand, the dissipativity is sought on a suitable bounded convex subset of the state space of solutions. This becomes difficult for the systems with infinite delay since in this case the subset is probably not forward invariant for the orbits of solutions. These are also considerable even for the usual functional differential equations with infinite delay. As an application, we answer an open problem on the existence of an equilibrium state for multivalued permanent systems.     

关于四阶常微分方程奇摄动边值问题的一个注记

给出Howes等人关于四阶常微分方程奇摄动边值问题解的存在性结果的一些反例. 这 些反例说明Howes等人的结果都是不正确的.     

偶数阶微分方程的两点边值问题

利用对称双线性型引理和Schauder不动点定理,本文对一类偶数阶非线性微分方程给出存在唯一性定理.