非线性两点边值问题有唯一解的几个判据

Several Criterions of the Nonlinear Two—Point Boundary Value Problems with Unique Solution

本文研究二阶非线性常微分文程 x″=f(t,x,x′) 在区间[0,1]上的第一和第二边值问题,在主要假设f_x≥—β(t)≥—,β(t),—a≤f_x′≤α(1+|x′|)的情形下,给出了第一、第二边值问题有唯一解的充分条件。

In this paper the first and second boundary problems in the interval [0, 1] of a second order nonlinear ordinary differential equation x'= f(t,x,x')are studied. In ease of f_x≥β(t)≥—, β(t)and—αf_x'≤α(1+|x'|) mainly, the sufficient conditions of the first and second boundary value problems with unique solution are given.