STRUCTURE OF POSITIVE SOLUTIONS OF A CLASS OF QUASILINEAR ORDINARY DIFFERENTIAL EQUATIONS

The existence and uniqueness of positive solutions for a class of quasilinearordinary differential equations with a large parameter are obtained. It is shownthat the flat core of positive solutions can exist. So some results of [1-3] aresharpened.     

ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF NONLINEAR DELAY DIFFERENTIAL EQUATIONS

Sufficient conditions are established for the asymptotic behavior of solutionsof nonlinear delay differential equations x′(t)+sum from i=1 to m(pi(t)x(t-т_i))=F(t,x_t),t≥0where 0<т_1<т_2<…<т_m≤r,pi∈C([0,∞)),i=1,2,…,m,F∈C([0,∞)×C_0,R).C_0=C([-r,0],R)equipped with the sup norm ||·|| forsome r>0. A new result is established, some known results are improved.     

几种广义非线性发展方程的新解

本文研究了构造了广义Kd V方程和广义KP-Burgers方程等几种广义非线性发展方程的新解的问题.利用三种辅助方程及其新解,获得了广义Kd V方程和广义KP-Burgers方程等几种广义非线性发展方程的新解.这些解由双曲余割函数、双曲正切函数、双曲正割函数、双曲余切函数和余割函数组成.     

关于一类非线性发展方程整体解的存在性问题

本文研究一类模拟非线性弹性杆的纵振动的非线性发展方程的初边值问题，证明了其整体解的存在性、唯一性、光滑性及在一定条件下，整体解的不存在性。     

QUALITATIVE ANALYSIS OF BOBWHITE QUAIL POPULATION MODEL

In this paper, the qualitative behavior of solutions of the bobwhite quail pop-ulation modelwhere 0   

广义Liénard系统周期解的不存在性

本文建立了广义Lienard系统不存在周期解的若干充分条件．     

二阶非线性中立型时滞差分方程的正解

本文研究了一类二阶非线性中立型时滞差分方程的正解,得到了最终正解的存在性判据及存在正解的必要条件,建立了一些正解不存在性定理,所得结论推广并改进了已知的一些结果。     

STUDY OF PERIODIC SOLUTIONS OF FOURTH ORDER NDE WITH DELAYS

Using Fourier series theory and techniques of real analysis inequality, some sufficient conditions of existence and uniqueness of periodic solutions for a class of fourth order neutral differential equations with some delays are obtained, the results extend and improve some known results.     

一类中立型时滞微分方程解的渐近性

本文考虑一类非线性中立型时滞微分方程解的渐近性，给出了方程的解收敛于常数的结果．所得结论改进和推广了文献中的某些已知结果．     

THE EXISTENCE AND UNIQUENESS OF THE SOLUTIONS OF DAES

1Intr0ducti0nDifferential-algebraicequations(DAEs)areveryusefu1inwidefields(cf.[1]).Bydifferential-algebraicequations,wemeanthoseequati0nswhosepartsof"derivative"cann0tbeexpressedexplicitly.Forexample,weconsidertheimplicitdifferentialequationwithmappingFsm00thssufficient1y.Itisusuallyreferredt0adifferential-algebraicequation(DAE)whentherank0fD.F(t,x,p)islessthann,wheretheremightbesomepurea1gebraic,whichwecallc0nstraintequations.TheDAEs,inparticular,theexistenceanduniquenessofitssolutions…     

高阶拟线性中立型偏泛函微分方程组解的振动性

1 引言 由于在人口动力学、生物遗传工程和化学反应过程等自然的和人为的过程中都存在滞后现象,因而偏泛函微分方程(组)的研究能更精确地揭示事物本质,同时能丰富微分方程(组)理论的研究。近十几年来,很多学者在泛函偏微分方程解的振动理论的研究方面作了大量工作,取得了许多成果。然而,关于泛函偏微分方程组解的振动性的研     

非线性中立型偏微分方程解的振动性

本文考虑了一类非线性中立型偏微分方程，获得了方程的所有解振动的充分条件，同时也给出了实际应用例子。     

关于一个吸放热系统解的存在性

本文讨论一个吸放热反应扩散系统及其平衡态的正解的存在性同Ｔｈｉｅｌｅ－模量间的依赖关系，同时得出解的某些性质。     

OSCILLATION FOR SOLUTIONS OF SYSTEMS OF N-TH ORDER PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper, some sufficient conditions for the oscillation for solutions to systems of n-th order partial functional differential equations are obtained.     

EVANS FUNCTIONS AND INSTABILITY OF A STANDING PULSE SOLUTION OF A NONLINEAR SYSTEM OF REACTION DIFFUSION EQUATIONS

In this paper, we consider a nonlinear system of reaction diffusion equations arising from mathematical neuroscience and two nonlinear scalar reaction diffusion equations under some assumptions on their coefficients. The main purpose is to couple together linearized stability criterion (the equivalence of the nonlinear stability, the linear stability and the spectral stability of the standing pulse solutions) and Evans functions to accomplish the existence and instability of standing pulse solutions of the nonlinear system of reaction diffusion equations and the nonlinear scalar reaction diffusion equations. The Evans functions for the standing pulse solutions are constructed explicitly.     

一类二阶差分方程边值问题解的存在性

本文研究了一个二阶差分方程边值问题解的存在性问题.利用临界点理论和变分方法,获得了几个解的存在性结果,推广了一些现有的结果.     

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.     

ON THE NON-EXISTENCE OF PERIODIC SOLUTIONS OF A GENERALIZED LIENARD SYSTEM

ＯＮＴＨＥＮＯＮ－ＥＸＩＳＴＥＮＣＥＯＦＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＯＦＡ　ＧＥＮＥＲＡＬＩＺＥＤＬＩＥＮＡＲＤＳＹＳＴＥＭＨｕａｎｇＬｉｈｏｎｇ（黄立宏）（ＨｕｎａｎＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒ，ｓｏｍｅｋｎ...     

ON THE UNIFORM DISSIPATIVITY OF SOME FIFTH-ORDER NON-LINEAR DIFFERENTIAL EQUATIONS

This paper studies the problem of uniformly dissipative solutions of somefifth order non-linear differential equations by the use of frequency domaintechnique. We use the generalized theorem of Yacubovich on dissipativity toobtain some new sufficient conditions of the existence of solutions that aredissipative for (1.1) and (1.2).     

OSCILLATION OF A CLASS OF HILLE EQUATION

This paper studies a class of Hille equation. A formula for solutions of a class of Hille equation is given. Under some suitable conditions the oscillation and nonoscillation of a class of Hille equation are established. Our results generalize the known Hille's ones.