EXISTENCE AND UNIQUENESS OF SOLUTION FOR FOURTH-ORDER NONLINEAR TWO-POINT BOUNDARY VALUE PROBLEM

In this paper, by using Leray-Schauder degree theory, we establish the existence and uniqueness theorems for a kind of fourth-order nonlinear two-point boundary value problem.     

奇异非线性二阶三点边值问题正解的存在唯一性

本文研究了一类奇异非线性二阶三点边值问题，通过摄动技巧和比较原理获得了所论问题正解的存在唯一性。     

EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR HIGHER ORDER NONLINEAR THREE-POINT BOUNDARY VALUE PROBLEMS

In this paper,by using Leray-Schauder degree theory,we establish the exi- stence and uniqueness theorems for some higher order nonlinear three-point boundary value problems.     

SINGULAR PERTURBATION OF THIRD ORDER NONLINEAR BOUNDARY VALUE PROBLEM WITH TWO TURNING POINTS

1IntroductionManyauthorshavedealtwiththeboundaryvalueproblemsofsecondorthirdorderdifferentialequationwithaturningpoint[l-5],butthatwithtwoormoreturningpointsisscarcelydiscussed.ThispaperconcernsthefollowingboundaryvalueproblemwhereE>0isasmallparameter,0,I…     

EXISTENCE AND UNIQUENESS THEOREMS FOR HIGHER-ORDER BOUNDARY VALUE PROBLEMS

An existence and uniqueness of solutions for boundary value problemsandare established, by employing a priori estimates for all solutions and the Schau-der fixed point theorem. Some of these results extend earlier results due toUsmani(1979), Yang(1988), and Pei(1997).     

ON THE EXISTENCE,MULTIPLICITY AND UNIQUENESS OF POSITIVE SOLUTION FOR A THIRD ORDER TWO-POINT BOUNDARY VALUE PROBLEM

The existence, multiplicity and uniqueness of positive solutions of a third order two point boundary value problem are discussed with the help of two fixed point theorems in cones, respectively.     

ASYMPTOTIC ESTIMatION OF ROBIN BOUNDARY VALUE PROBLEM FOR THIRD NONLINEAR EQUATION

1IntroductionThepreviousworks,forexample,theref',renccsll,21,havedis(fusscdthoboundaryvalueproblemswitlltwopointboundarycondition.Inthispaper,weconsiderRobinbonn(laryvalueproblemofthefornltheexistenceandasymptoticestimationofsolutionareestablished.Where2…     

EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTION FOR NONLINEAR SINGULAR 2mth-ORDER CONTINUOUS AND DISCRETE LIDSTONE BOUNDARY VALUE PROBLEMS

By fixed point theorem of a mixed monotone operators, we study Lidstone boundary value problems to nonlinear singular 2mth-order differential and difference equations, and provide sufficient conditions for the existence and uniqueness of positive solution to Lidstone boundary value problem for 2mth-order ordinary differential equations and 2mth-order difference equations. The nonlinear term in the differential and difference equation may be singular.     

二阶非线性边值问题解的存在唯一性定理

考虑方程ｙ‘’＋ｆ（ｔ，ｙ，ｙ‘）＝０在边值条件ｙ（ａ）＝Ａ，ｙ（ｂ）＝Ｂ下解的存在唯一性，要求ｆ满足Ｌ＾２－Ｃａｒａｔｈｅｏｄｏｒｙ条件，在Ｌ＾２空间中利用映象原理得到解唯一存在的最优结果。     

EXISTENCE OF POSITIVE SOLUTIONS TO A SINGULAR THIRD-ORDER THREE-POINT BOUNDARY VALUE PROBLEM

In this paper, we study a singular third-order three-point boundary value problem. By using a fixed-point theorem of cone expansion-compression type, we establish results on the existence of at least one, at least two, and $n$ positive solutions to the boundary value problem. Finally we give an example.     

具有两参数的非线性椭圆型方程边值问题解的渐近性态

讨论一类具有双参数的非线性椭圆型方程边值问题. 引入多重尺度变量, 构造问题的形式渐近解. 利用微分不等式理论, 证明边值问题渐近解的存在性和一致有效性. 由解的结构指出, 在两参数一定的情况下,相应问题的解只具有一个边界层.     

EXISTENCE OF SOLUTIONS TO A THIRD-ORDER THREE-POINT BOUNDARY VALUE PROBLEM

In this paper,we study the existence of solutions to a third-order three-point boundary value problem.By imposing certain restrictions on the nonlinear term,we prove the existence of at least one solution to the boundary value problem by the method of lower and upper solutions.We are interested in the construction of lower and upper solutions.     

A SINGULARLY PERTURBED EIGENVALUE ROBIN PROBLEM WITH TURNING POINT OF HIGHER ORDER

A singularly perturbed eigenvalue Robin problem with turning point of higher order is studied, which can describe some heat conduction phenomena. Using the method of Langer transformation, the uniformly asymptotic solution of the equation is obtained, which is expressed by Bessel function, and the eigenvalue and eigenfunction of the problem are given, and then the known result is generalized.     

在局部区域上的奇摄动非线性方程Robin边值问题

本文是讨论一类在局部区域上的奇摄动非线性Robin边值问题。利用算子理论和不动点原理，得到了相应问题解的存在性和唯一性。     

THE BOUNDARY VALUE PROBLEMS OF A CLASS OF ELLIPTIC EQUATION WITH A CURVE OF TURNING POINT

The boundary value problems of a class of elliptic equation with a curveof turning point are considered. Using the method of multiple scales and thecomparison theorem, the asymptotic behavior of solution for the boundary valueproblem is studied.     

三阶非线性常微分方程非线性两点边值问题解的存在性与唯一性

本文得用Ｂｏｌｚａｎｏ定理，给出了三阶非线性常微分方程具非线性两点边界条件的边值问题（１）（２）存在解与存在唯一解的一般结果，并将所得结果应用于Ｌｉｐｓｃｈｉｔｚ方程，对Ｌｉｐｓｃｈｉｔｚ方程满足（２），（３）的边值问题给出了解存在与存在唯一解的较具体的充分条件。     

二阶非线性积分微分方程组边值问题解的渐近式

研究n-维二阶非线性向量积分微分方程组边值问题的奇摄动,在适当的条件下,利用改进了的对角化方法、逐步逼近法和不动点定理,求得并证明非线性向量积分微分方程组边值问题解的存在性及其渐近表达式,并给出渐近估计.     

BOUNDARY AND CORNER LAYER BEHAVIOR IN SINGULARLY PERTURBED ROBIN BOUNDARY VALUE PROBLEM

This paper is concerned with boundary and corner layer behavior of the singularly perturbed Robin boundary value problem(RP) for the second-order nonlinear differential equations. The existence and asymptotic estimate of solutions of (RP) is discussed by appropriately constructing the bounding functions and using the theory of differential inequality.