有界洞型区域内一类半线性椭圆型方程边值问题的可解性

Solvability for Certain Semi Linear Elliptic Equations Boundary Value in the Bounded Domain with a Hole

半线性椭圆型方程边值问题是一个重要问题,本文利用不动点定理和极值原理,研究了有界洞型区域内一类半线性椭圆型方程边值问题解的存在性与唯一性。当这类问题给定的函数满足特定条件时,问题就有解,作为定理的应用,给出了一个实例。

A class of semi linear elliptic equations is an important problem.Uniqueness and existence of the positive solutions to a class of semi linear elliptic equations are proved by using of fixed-point theorem and the extreme value theorem.When a given function satisfies certain conditions,the problem is solved.As the application of the theorem,an example is given.