一类半线性椭圆型方程边值问题的可解性

Solvability of boundary value problems of a class of semi-linear elliptic equations

在偏微分方程研究领域中,对半线性椭圆型方程边值问题的研究一直是主要研究方向之一,特别是半线性椭圆型方程边值问题正解的研究热点不断;该文利用Levay-Schauder不动点定理研究了一类半线性椭圆方程在有界正则域中正解的存在性、不存在性以及解的唯一性,作为定理的应用,给出了一个应用实例。

The boundary value of semi-linear elliptic equations has always been one of the major orienta-tions in the research on partial differential equations, and the research on the positive solutions to the boundary value of semi-linear elliptic equations has been one of the hot topics in the field. In this paper, the existence, nonexistence and uniqueness theorems of positive solutions to a class of semi-linear elliptic equations are proved by using the Levay-Schauder fixed point theorem and three lemmas. Here ΩìR^n（n≥2） is a boundary regular regioru As the application of the theorems, an example is given.