椭圆型边值问题的比较方法及解的存在性

Existence of solution and compare method of elliptic boundary value problems

利用上、下解方法及不动点理论研究了一类反应项非单调的椭圆型方程组,构造了非单调反应项的上、下控制函数,并证明了所构造的函数满足L ipsch itz条件及单调性,为讨论反应项非单调的微分方程提供了一种有效方法,获得了此系统边值问题解的存在性,并推广了已有的一些结果.

In this paper,elliptic boundary value problems are investigated, By constructing me upper lower control functions of nonmonotone reaction term, and we prove that the functions satisfy a global Lipschitz condition and quasimonotone. A sort of effective method of studying differential equation with nonmonotone reaction term is gained. By using the method of upper and lower solutions and fixed point theorem, we also prove that solution of this system exists when reaction - term is not monotone and the boundary value system has a pair of coupled upper and lower solutions. And some known results are extended.