一类二阶非线性常微分方程组边值问题解的存在唯一性

Existence and uniqueness of solutions for boundary value problem of second-order nonlinear ordinary differential systems

本文讨论如下二阶非线性常微分方程组边值问题{-u″(t)=f(t,u(t),v(t)),t∈[0,1],-v″(t)=g(t,u(t),v(t)),t∈[0,1],u(0)=u(1)=0,v(0)=v(1)=0解的存在唯一性,其中f,g:[0,1]×R×R→R连续.当非线性项f(t,x,y)与g(t,x,y)满足相应的不等式时,本文运用Leray-Schauder不动点定理获得了该问题解的存在唯一性.

This paper discusses the existence and uniqueness of solutions for the following second-order nonlinear ordinary differential equations boundary value problems:{-u″(t)=f(t,u(t),v(t)),t∈[0,1],-v″(t)=g(t,u(t),v(t)),t∈[0,1],u(0)=u(1)=0,v(0)=v(1)=0,where f,g:[0,1]×R×R→R are continuous.By applying the Leray-Schauder fixed point theorem,we obtain the existence and uniqueness of solutions under an inequality condition on the nonlinear term f(t,x,y)and g(t,x,y).