OSCILLATORY AND ASYMPTOTIC BEHMIOUR OF A CLASS OF NONLINEAR DIFFERENTIALEQUATIONS OF THIRD ORDER

1IntroductionInthispaperwedealwithoscillatoryandnonoscillatorybehaviourofsolutionsofnonlinearthirdorderdifferentialequationsoftheformwherea,b,cEC([er,co),R),rrER,fEC(R,R)suchthatac2P>0fory/0and7>0isaquotientofoddintegers.From"Theoryofequations"tsee[1],itfollowsthattheequationwithconstantcoefficientsMoreover,allnonoscillatorysolutionsof(1.3)tendtozeroifandonlyifequatioll(l.3)hasanoscillatorysolution.Theseobservationsarefoundtobetruetoalargeextentformoregeneralequationsoftheformwherealb,cE…     

动力系统中一类二阶非线性微分方程解的存在性

本文讨论了动力系统中一类二阶非线性微分方程的边值问题，获得并证明了这些问题的解的存在定理。     

一类两相Stefan问题的弱解的局部存在性

本文讨论一维情形下一类两相Ｓｔｅｆａｎ问题，证明了弱解的局部存在性。     

线性规划最优解集的表现

文献［１］讨论了有无穷多最优解的线性规划问题，并利用最优单纯形表格的检验数给出线性规划有无穷多最优解的判别法，本文利用最优基可行解的凸组合及最优极向的非负线性组合给出线性规划最优解集的表现，从而把线性规划最优解集的几何特征阐释清楚．     

LONG-TIME BEHAVIOR OF A CLASS OF REACTION DIFFUSION EQUATIONS WITH TIME DELAYS

The present paper devotes to the long-time behavior of a class of reaction diffusion equations with delays under Dirichlet boundary conditions. The stability and global attractability for the zero solution are provided, and the existence, stability and attractability for the positive stationary solution are also obtained.     

EXISTENCE OF PERIODIC SOLUTIONS OF THE BURGERS-GINZBURG-LANDAU EQUATIONS

In this paper, the existence of the periodic solutions for a forced Burgers equation coupled to a non-homogeneous Ginzburg-Landau equation is proved by Leray-Schauder fixed point theorem and Galerkin method under appropriate conditions.     

r-循环线性系统求解的快速算法

本文给出r-循环线性系统求解的一种快速算法.当r-循环矩阵非奇异时,该快速算法求出该线性系统的唯一解;当r-循环矩阵奇异时,该快速算法求出该线性系统的通解.     

BIFURCATIONS OF TRAVELLING WAVE SOLUTIONS TO A COUPLED NONLINEAR WAVE SYSTEM

Employ theory of bifurcations of dynamical systems to a system of coupled nonlin-ear equations, the existence of solitary wave solutions, kink wave solutions, anti-kink wave solutions and periodic wave solutions is obtained. Under different parametric conditions, various suffcient conditions to guarantee the existence of the above so-lutions are given. Some exact explicit parametric representations of travelling wave solutions are derived.     

GLOBAL EXISTENCE OF THE SOLUTION FOR THE LANDAU-LIFSHITZ EQUATION OF THE FERROMAGNETIC SPIN CHAIN

1IntroductionInthepresentpaper,wecollsidertileLandau-LifSllitzequationoftileferromagneticspinchainwhichtakestheform:where"x'ldenotesthevectorcrossproductinR',fi=(--D,D),D>0,u=(ul,u3,u3):fixR -R3istilespinvector,or>0isaGilbertdampingconstant,Pisarealparameter,J=diag(ri,acfac)isaconstantmatrix.TheaboveequationarisesinthedoublyanisotropicHeisenbergspinsystem.Thissystemisimpliedbytileconservationofenergyandmagnitudeofu.SeeDanielandLab.hmanan[1]please.Insomeferromagneticchainsystems,thematri…     

GLOBAL EXISTENCE OF SOLUTIONS OF CAUCHY PROBLEM FOR GENERALIZED BBM-BURGERS EQUATION

In this paper, the existence and the uniqueness of the local generalized solution and the local classical solution of the Cauchy problem for the generalized BBM-Burgers equationare proved. The existence and the uniqueness of the global generalized solution and the global classical solution for the Cauchy problem of equation （1） are proved when n = 3, 2, 1. Moreover, the decay property of the solution is discussed.     

一类具有无穷时滞竞争扩散模型的周期解的存在性

本文研究了一类具有无穷时滞竞争扩散模型的周期解问题,采用了上下解的方法,获得了周期解的存在性,并给出了解的渐近性态.     

高维系统周期解的共振分支

本文利用Liapunov－Schmidt方法获得了高维自治系统在共振情况下决定周期解个数的分支函数，并通过计算分支函数的主项，分析分支函数的零点，研究了具两对共轭特征根的四维系统多个周期解的共振分支问题．     

ON MEROMORPHIC SOLUTIONS OF A TYPE OF SYSTEM OF COMPOSITE FUNCTIONAL EQUATIONS

In this article,we mainly investigate the growth and existence of meromorphic solutions of a type of systems of composite functional equations,and obtain some interesting results.It extends some result...     

A NECESSARY AND SUFFICIENT CONDITION OF EXISTENCE OF GLOBAL SOLUTIONS FOR SOME NONLINEAR HYPERBOLIC EQUATIONS

ＡＮＥＣＥＳＳＡＲＹＡＮＤＳＵＦＦＩＣＩＥＮＴＣＯＮＤＩＴＩＯＮＯＦＥＸＩＳＴＥＮＣＥＯＦＧＬＯＢＡＬＳＯＬＵＴＩＯＮＳＦＯＲＳＯＭＥＮＯＮＬＩＮＥＡＲＨＹＰＥＲＢＯＬＩＣＥＱＵＡＴＩＯＮＳ￥ＺＨＡＮＧＱＵＡＮＤＥ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅ...     

高维非自治系统非平凡周期解的存在性

本文利用非线性泛函分析中锥的理论，讨论了ｎ维非自治系统ｘ＝Ａ（ｔ）ｘ＋ｇ（ｔ，ｘ）ｘ∈Ｒ＾ｎ产工得到了系统（１）存在非平凡ω周期解的充分条件。     

WEAK SOLUTIONS OF MONGE-AMPIERE TYPE EQUATIONS IN OPTIMAL TRANSPORTATION

This paper concerns the weak solutions of some Monge-Amp~re type equa- tions in the optimal transportation theory. The relationship between the Aleksandrov solutions and the viscosity solutions of the Monge-Ampere type equations is discussed. A uniform estimate for solution of the Dirichlet problem with homogeneous boundary value is obtained.     

不稳定型二阶中立型方程正解的存在性与有界振动

本文研究一类不稳定型二阶中立型微分方程正解的存在性与有界振动．证明了在一定条件下不稳定型二阶中立型方程总存在无界正解，并给出了保证其方程的一切有界解都振动的充分条件，改进了文［１，２］中的有关条件．     

UNIQUENESS OF STATIONARY SOLUTIONS WITH VACUUM OF EULER-POISSON EQUATIONS

In this paper, the uniqueness of stationary solutions with vacuum of Euler-Poisson equations is considered. Through a nonlineax transformation which is a functionof density and entropy the corresponding problem can be reduced to a semilinear ellipticequation with a nonlinear source term consisting of a power function, for which the classical     

一类复函数方程组的亚纯解

本文研究了一类复函数方程组的亚纯解的存在性问题.利用亚纯函数的Nevanlinna值分布理论,得到了有关方程组的亚纯解变成了有理解的一个主要结论,将复函数方程的某些结果推广至复函数方程组中.     

BOUNDEDNESS OF POSITIVE SOLUTIONS OF THE CONFORMAL SCALAR CURVATURE EQUATION AND POSITIVE SCALAR CURVATURE

We study the boundedness of positive solutions of the conformal scalar curvature equation in a complete Riemannian manifold, in connection with conformal metrics of strictly positive scalar curvature.