一类非线性二阶椭圆型方程组的正解

Positive Solution for a Class of Systems of Nonlinear Elliptic Equations of Second Order

本文讨论二阶非线性椭圆边值问题的正解的存在性,其中非线性项f和g关于u,v的增长限制很不相同.f是超线性的,而g满足次线性的条件.利用拓扑度理论和上、下解方法,得到了几个正解的存在性定理.作为应用,本文还给出了一些具体的例子.

In this paper,the following boundary problem for a system of semilinear elliptic equations is considered,where the nonlinear term f is superlinear and g satisfies the conditions of sublinear or other conditions which are not superlinear. So the nonlinear growth of f and g are much different. Using the method of supersolution and subsolution and the theory of topology degree,we obtain some existence results of positive solution. In the end,some examples as applications are given.