非线性项依赖于一阶导数的共振情形下二阶三点边值问题解的存在性和唯一性

Existence and Uniqueness of Three-point Boundary Value Problem at Resonance with Nonlinear Term Depending on the First Order Derivative

本文致力于研究共振情形下二阶三点边值问题x″(t)+f(t,x(t),x′(t))+0,t∈(0,1)x(0)=0,x(1)=ζx(η)其中f:[0,1]×R^2→R是一个连续函数,ζ>0,0<η<1满足ζη=1运用先验界估计,微分不等式技巧和Leray-Schauder度理论得到了该边值问题解的存在性和唯一性.

This paper is devoted to studying,the second-order three point boundary value problem ar resonance x＂（t） ＋ f（t,x（t）,x＇（t）） =0,t∈（0,1）, x（0） = 0,x：（1） =ξx（η）, where f：[0,1]×R^2→R is continuous,ξ0,0η1 such thatξη=1.The existence and uniqueness of solution of the boundary value problem are given by using priori estimates, differential inequalities technique and Leray-Schauder degree theory.