Existence of solutions for a class of third-order two-point boundary value problems(一类三阶两点边值问题解的存在性)

Abstract

In this paper, we consider the boundary value problems of third-order nonlinear ordinary differential equation u'''t=f(t,u(t),u'(t),u''(t)), a.e. 0<t<1,u0=u'0=u'1=0,where f:[0，1]×R3→R satisfies Carathéodory conditions. Under some suitable growth conditions on f, we show that the above problem has at least one solution. The proof of the main results is based on Leray-Schauder fixed point theorem.(考察了三阶非线性常微分方程边值问题u'''t=f(t,u(t),u'(t),u''(t)), a.e. 0<t<1,u0=u'0=u'1=0,其中f:[0，1]×R3→R 满足Carathéodory条件。在非线性项 f 满足适当增长性条件下，三阶非线性常微分方程边值问题至少存在1个解。基于Leray-Schauder不动点定理证明了主要结果。)

Keywords

• third-order ordinary differential equation(三阶常微分方程)
• boundary value problem(边值问题)
• leray-schauder fixed point theorem(leray-schauder不动点定理)
• existence(存在性)