一类二阶三维微分方程组边值问题正解的存在性

The Existence of Positive Solutions of a Class of Boundary Value Problems for Systems of Second Order Three-dimensional Differential Equations

利用锥拉伸锥压缩不动点定理,研究了下列二阶三维微分方程组边值问题:-u″=f(t,u,v,w)-v″=g(t,u,v,w)-w″=h(t,u,v)u(0)=u(1)=v(0)=v(1)=w(0)=w(1)=0在满足某些条件下正解的存在性。

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