关于一类非线性微分方程组的边值问题的渐近解（Ⅰ）

应用新的方法 ,研究一类非线性微分方程组　　u″ =v,εv″ f(x ,u ,u′)v′ -g(x ,u ,u′)v =0　　 (0 <ε 1) ,的边值问题的解的渐近性质·　构造出解的渐近展开式 ,和估计了余项 ,改进并拓广了前人的工作·     

一类含参数半正四阶边值问题的正解存在性与多解性

考察了一类含有两个参数的非线性四阶边值问题的n个解和/或正解的存在性,其中允许非线性项有一个非正的函数型下界.在力学和工程上,这类四阶边值问题描述了两端简单支撑的弹性梁的变形.主要工具是锥上的Krasnosel’skii不动点定理和局部化方法.     

THE SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM OF NONLINEAR INTEGRO-DIFFERENTIAL SYSTEM

In this paper, using the differential inequality and singularly perturbed theory, the singularly perturbed boundary value problems for nonlinear integro-differential system has been studied. Under some appropriate assumptions, the existence of solution has been proved and the uniform validness of the asymptotic expansions for arbitrary nth-order have been obtained simply and conveniently.     

几类高阶非线性两点边值问题的可解性

主要利用Leray-Schauder原理研究了几类高阶非线性两点边值问题解的存在性.     

Solvability for a nonlinear second-order three-point boundary value problem

This paper investigates the existence of nontrivial solution for the three-point boundary value problem

     

线性增长条件下一类非线性梁方程解的存在性

考察了一类非线性四阶两点边值问题的解的存在性.通过构造适当的Banach空间并且利用积分方程建立了一个存在定理.主要工具是Leray-Schauder非线性抉择.本文表明,如果非线性项在其定义域的某个有界子集上的增长速度是线性的,该问题可能存在解.     

Solvability of Third-order Three-point Boundary Value Problems with Carathéodory Nonlinearity

A class of third-order three-point boundary value problems is considered,where the nonlinear term is a Carathéodory function.By introducing a height function and considering the integration of this hei...     

Solvability of Third-Order Three-Point Boundary Value Problems with Carathéodory Nonlinearity

A class of third-order three-point boundary value problems is considered, where the nonlinear term is a Carathéodory function. By introducing a height function and considering the integration of this height function, an existence theorem of solution is proved when the limit growth function exists. The main tools are the Lebesgue dominated convergence theorem and the Schauder fixed point theorem.     

On initial value problems related to p-Laplacian and pseudo-Laplacian

Summary We establish some qualitative properties in the sense of weak singularity and super singularity for a certain system of two nonlinear differential equations related to the radially symmetric solution of p-Laplacian and pseudo-Laplacian problems. For the transformed system of differential equations we carry out the classification in the sense of weak singularity, singularity and super singularity. The choice of initial values at the point of singularity for correct settings of Cauchy problem is also considered.     

On the index of the boundary value problem for a homogeneous Hamiltonian system of differential equations

The index of the homogeneous self-adjoint boundary value problem for the Hamiltonian systems of ordinary differential equations is introduced. It is assumed that the system has a nontrivial solution. The relationship between the index of an eigenvalue of the nonlinear eigenvalue problem and the index of the corresponding homogeneous problem is established. Properties of the index of the problem and those of the eigenvalue are examined.     

高阶非线性多点边值问题解的存在性与唯一性

In this paper, the existence and uniqueness theorems of solutions of k-point boundary value problems for nth-order nonlinear differential equations are established by Leray-Schauder continuation theorem.     

一类强非线性奇摄动边值问题

In this paper, a class of strongly nonlinear singular perturbed boundary value problems are coasidered by the theory of differential inequalities and the correction of boundary layer, under which the existence of solution is proved and the uniformly valid asymptotic expansions is obtained as well.     

EXISTENCE AND ASYMPTOTIC ESTIMATE OF SOLUTION FOR THIRD ORDER BOUNDARY VALUE PROBLEM

This article shows the existence and asymptotic estimates of solutions of singularly perturbed boundary value problems for a class of third order nonlinear differential equations εx'" = f(t,x,x',ε), x(0) = A, x'(0) = x'(1), x"(0) = x"(1).     

一类奇摄动非线性Volterra型泛函微分方程边值问题

Abstract. In this paper,a kind of boundary value problems for Volterra functional differential e-quation is studied.     

非线性悬臂梁方程的正解存在定理

研究了非线性悬臂梁方程u^（4）（t）=f（t,u（t）,u′（t））,0相似文献   

奇摄动非线性系统边值问题*

本文利用对角化技巧和方法讨论二阶奇摄动非线性系统边值问题εy"＝f(t,y,y',ε),y(0,ε)＝α(ε),y(1,ε)＝b(ε)当Jacobi矩阵fy'的特征值有K个负实部和N－K个正实部时,解的存在性及其渐近性质。     

Existence and Regularity of Solutions of a Nonlinear Nonuniformly Elliptic System Arising from a Thermistor Problem

A thermistor is an electric circuit device made of ceramic material whose electric conductivity depends on the temperature. If the only heat source is the electric heating, the temperature and the electric potential satisfy a nonlinear elliptic system which is also degenerate if the electric conductivity is not uniformly bounded from above or away from zero. Under general boundary conditions, we establish existence and Hölder continuity of solutions of such a nonlinear nonuniformly elliptic system. When the elechic conductivity linearly depends on the temperature, we provide a non-uniqueness and non-existence example.     

A method of solving a nonlinear boundary value problem with a parameter for a loaded differential equation

A nonlinear loaded differential equation with a parameter on a finite interval is studied. The interval is partitioned by the load points, at which the values of the solution to the equation are set as additional parameters. A nonlinear boundary value problem for the considered equation is reduced to a nonlinear multipoint boundary value problem for the system of nonlinear ordinary differential equations with parameters. For fixed parameters, we obtain the Cauchy problems for ordinary differential equations on the subintervals. Substituting the values of the solutions to these problems into the boundary condition and continuity conditions at the partition points, we compose a system of nonlinear algebraic equations in parameters. A method of solving the boundary value problem with a parameter is proposed. The method is based on finding the solution to the system of nonlinear algebraic equations composed.     

Blow-up vs.Global Finiteness for an Evolution p-Laplace System with Nonlinear Boundary Conditions

In this paper, the authors consider the positive solutions of the system of the evolution p-Laplacian equations
with nonlinear boundary conditions
and the initial data （u0, v0）, where Ω is a bounded domain in Rn with smooth boundary δΩ, p 〉 2, h（·,·） and s（·,· ） are positive C1 functions, nondecreasing in each variable. The authors find conditions on the functions f, g, h, s that prove the global existence or finite time blow-up of positive solutions for every （u0, v0）.