一个n阶微分方程的两点边值问题

Two-point Boundary value Problems for n-order nonlinear differential equation

有一些n阶非线性微分方程的两点边值问题已被人们讨论过,大多是在微分方程的右端函数有界、满足李普希兹条件或在相应边值问题存在上下解的情况下讨论的。[3]、[4]在这篇文章里,讨论了一个n阶非线性微分方程的两点线性边值问题,是首先通过n-2次累次积分将原方程化成了一个二阶微积分方程边值问题,并用拓扑度理论讨论了解的存在性,同时给出了解的唯一性条件。推广了文献[1]的结果。

Some two point boundary problems for n - order nonlinear differential equations were discussed. Most of these problems were based in boundary of right side land function for the differ ential equation and satisfying Lipschitz condition or the existence of supper and lower solutions for corresponding boundary value problem. In this paper we study two point linear boundary problem for n - order nonlinear differential equation whose right side land functions satisfying another class of conditions. We first obtain boundary value problem for 2 - order integral differential equation problem by applying （n- 2）times repeated integral of the equation. Further we establish the existence of solution by using topological degree theory and give the condition of uniqueness for the solution. Our results extend the corresponding results in Document[ 1 ].