非线性一阶常微分方程解的存在惟一性

Existence and uniqueness of solutions for first-order nonlinear ordinary differential equations

讨论了一类非线性一阶常微分方程边值问题解的存在惟一性.得到了当参数在一定的范围取值时解存在惟一的充分条件,并包含了一些已知结果.主要结果基于Leray-Schauder非线性抉择理论和Banach不动点定理.

In this paper, we show the existence and uniqueness of solutions of first-order nonlinear ordinary differential equation boundary value problem. The sufficient conditions for the existence and uniqueness of solutions are obtained when the parameter belongs to appropriate intervals, and we include some known results. The main results are based upon Leray-Schauder nonlinear alternative theorem and Banach＇s fixed point theorem.