BOUNDARY VXLUE PROBLEMS FOR SYSTEMS OF NONLINEAR SECOND ORDER DIFFERENTIAL DFFERENCE EQUATIONS

ＢＯＵＮＤＡＲＹＶＸＬＵＥＰＲＯＢＬＥＭＳＦＯＲＳＹＳＴＥＭＳＯＦＮＯＮＬＩＮＥＡＲＳＥＣＯＮＤＯＲＤＥＲＤＩＦＦＥＲＥＮＴＩＡＬＤＦＦＥＲＥＮＣＥＥＱＵＡＴＩＯＮＳ￥ＭＩＡＯＳＨＵＭＥＩＡｂｓｔｒａｃｔ：Ｔｈｅａｕｔｈｏｒｓｔｕｄｉｅｓｔｈｅｂｏｕ...     

四阶非线性常微分方程非线性两点边值问题解的存在唯一性

本文利用Ｂｏｌｚａｎｏ定理，给出了四阶非线性常微微分方程具有非线性边界条件的两点边值问题（１）（２）２，（１）（２）３存在解与存在唯一解的一般性结果，并将所得结果应用于Ｌｉｐｓｃｈｉｚ方程，对Ｌｉｐｓｃｈｉｔｚ方程满足边界条件（２）２，（２）３的边值问题给出了存在解与存在唯一解的具体的充分条件。     

二阶微分方程边值问题的多重正解

基于Leray-Schauder度理论和上下解方法讨论非线性边值问题(t)+g(t,y)=0,(0)=0,y(1)=b≥0的正解存在性,其中g局部Lipschitz连续,g(t,0)≥0,但是可以是变号函数。主要结论是:如果g(t,y)在y=+∞满足一个超线性增长条件,并且存在使得β(1)>0的非负上解β,则存在正数B使得当0B时,不存在正解。     

二阶奇异泛函微分方程的两点边值问题

本文研究具有Ｒｏｂｉｎ边界条件的二阶奇异泛函微分方程组Ａ（ｔ,ｘ,ｘ）ｘ＝ｆ（ｔ,ｘｔ,ｘｔ）的两点边值问题,给出该两点边值问题的两个解的先验估计定理和一个解的存在定理．     

BOUNDARY VALUE PROBLEMS FOR THIRD ORDER DIFFERENTIAL EQUATIONS

ＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＦＯＲＴＨＩＲＤＯＲＤＥＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ王金枝内蒙古大学，邮编：０１００２１ＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＦＯＲＴＨＩＲＤＯＲＤＥＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩ...     

二阶拟线性微分方程组边值问题的三个对称正解

本文讨论二阶拟线性微分方程组边值问题( p(x'))'+a(t),(t,x,y)=0,( q(y'))'+b(t)g(t,x,y)=0,x(0)-B0(x'(0))=x(1)+Bo(x'(1))=0,y(0)-B1(y'(0))=y(1)+B1(y'(1))=0,其中f,g是非负连续的函数.利用五个泛函的不动点定理,赋予f和g一些增长条件保证至少三个对称正解的存在性.     

SINGULAR PERTURBATION OF THREE-POINT BOUNDARY VALUE PROBLEM FOR THIRD ORDER DIFFERENTIAL EQUATIONS

In this paper, by the theory of differential inequalities, we study the existence and uniqueness of the solution to the three-point boundary value problem for third order differential equations. Furthermore we study the singular perturbation of three-point boundary value problem to third order quasilinear differential equations, construct the higher order asymptotic solution and get the error estimate of asymptotic solution and perturbed solution.     

二阶离散边值问题的一个存在性定理

作者利用监界点理论中的山路引理研究了一类非线性二阶差分方程边值问题解的存在性,获得了该边值问题有解的一个充分条件.     

COMPARISON THEOREMS TO BOUNDARY VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS

ＣＯＭＰＡＲＩＳＯＮＴＨＥＯＲＥＭＳＴＯＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＦＯＲＯＲＤＩＮＡＲＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ￥ＬＩＹＯＮＧ；ＷＡＮＧＨＵＡＩＺＨＯＮＧＡｂｓｔｒａｃｔ：Ａｕｎｉｆｉｅｄａｐｐｒｏａｃｈｉｓｇｉｖｅ...     

Banach空间中二阶非线性脉冲微分方程的Sturm-Liouville边值问题的极解

本文利用单调迭代技巧 ,锥理论和比较定理获得了Banach空间中二阶非线性脉冲微分方程的Sturm Liouville边值问题的极解     

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.     

一类半导体方程混合初边值问题解的渐近性

考虑在磁场影响下一类半导体方程的混合边值问题，在一定条件下，利用Ｍｏｓｅｒ技巧和先验估计，证明了瞬态解的存在性和平衡解的存在唯一性，经过一系列估计，证明了瞬态解的渐近性。     

PERIODIC BOUNDARY VALUE PROBLEM FOR SECOND ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS

This paper investigates the periodic boundary value problems for a class of second order functional differential equations. The monotone iterative technique and the maximum principle are applied to obtain the existence of maximal and minimal solutions.     

奇异二阶泛函微分方程边值问题的多重正解

本文把ＺｈａｏｌｉＬｉｕ和Ｅｒｂｅ等人关于常微分方程边值问题多重正解的工作推广到二阶奇异混合型泛函微分方程边值问题,证明了所考虑的方程边值问题存在至少两个正解的充分条件。     

A KIND OF SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM FOR NONLINEAR VOLTERRA FUNCTIONAL DIFFERENTIAL EQUATIONS

§ 1　IntroductionSince 1 970 the perturbed boundary value problems for functional differential equationshave been derived in many fields,such as biology,physics,optimal control and e-conomies[1 ] .Some works on studying it have appeared,for example references[2～ 6] .Inthis paper,we study a kind of singularly perturbed boundary value problems for Volterrafunctional differential equations:εx″(t) =f(t,x(t) ,[Tx] (t) ,x(t-τ) ,x′(t) ,ε) ,t∈ (0 ,1 ) ,(1 )x(t) =φ(t,ε) ,t∈ [-τ,0 ] ,ax(1 )…     

NONLINEAR BOUNDARY VALUE PROBLEMS FOR FIRST ORDER DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENTS

The authors employ the method of upper and lower solutions coupled with the monotone iterative technique to obtain some results of existence and un-iqueness for nonlinear boundary value problem of differential equations with piecewise constant arguments.     

PERIODIC BOUNDARY VALUE PROBLEMS FOR FIRST ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper, we investigate the periodic boundary value problems for nonlinear first order functional differential equations. By establishing a new comparison result, criteria on the existence of maximal and minimal solutions are obtained.     

ON THE SOLVABILITY OF NONLINEAR BOUNDARY VALUE PROBLEMS FOR FUNCTIONAL DIFFERENTIAL EQUATIONS

Sufficient conditions are established for the solvability of the boundary value problem where p : C(I; R ⁿ) × C(I; R ⁿ) L(I; R ⁿ), q : C(I; R ⁿ) L(I; R ⁿ), l : C(I, R ⁿ) × C(I; R ⁿ) R ⁿ, and c _n : C(I, R ⁿ) R ⁿ are continuous operators, and p(x, ) and l(x, ) are linear operators for any fixed .     

BOUNDARY VALUE PROBLEMS FOR nTH ORDER RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS

1IntroductionTherearemanyresultsofstudyingboundaryvalueproblemsforsecondorderfunctionaldifferentialequations['I'].Butthestudyofboundaryvalueproblemsforhigherorderfunctionaldifferentialequationsrarelyappears.Inthispaper,wediscussthefollowingntypesofboundaryvalueproblemsforniborderfunctionaldifferentialequationswheref(t,yi,xo3xl)'',x.--1)isacontinuousrealfunctiondefinedonthesetA=[0,T]xCdxR.Forafixedr>0,letCrgC([--r,0],R)bethespaceofcontinuousfunctionon[--r,0]withthenormdefinedbyIIWll=supl…     

二阶常微分方程及Thomas－Fermi方程的边值问题

本文利用上、下解方法推广了Ｍ．Ｌｅｅｓ关于半线性边值问题的结果，给出了另一类边值问题解的存在唯一性的一个充分条件；并利用所得的结果证明了Ｔｈｏｍａｓ－Ｆｅｒｍｉ方程的边值问题解的存在唯一性，从而推广了Ｃ．ＤＬｕｎｉｎｇ的结果．