一类三维二阶常微分方程组边值问题正解的存在性

Existence of positive solutions of a class of boundary value problems for systems of 3-dimensional second order ordinary differential equations

利用Krasnonel'skii不动点定理,研究了二阶微分方程组{-u″=a(t,w)f(u,v),-v″=b(t,w)g(u,v),-w″=h(t,u,v),u(0)=u(1)=v(0)=v(1)=w(0)=w(1)=0的边值问题在某些条件下正解的存在性.

This paper is concerned with the existence of positive solutions of a class of boundary value problems for systems of second order ordinary differential equations {-u″=a（t,w）f（u,v）, -v″=b（t,w）g（u,v）, -w″=h（t,u,v）, u（0）=u（1）=v（0）=v（1）=u（0）=w（1）=0 Under the suitable conditions, the existence of positive solutions is established by using the Krasnonel＇skii＇s fixed point theorem.