一类二阶半线性椭圆型边值问题解的存在唯一性  

On Existence and Uniqueness of Solutions of a Class of Second Order Semilinear Elliptic Boundary Value Problems

作　　者：游雄[1] 

机构地区：[1]南京农业大学理学院,江苏南京210095

出　　处：《四川师范大学学报（自然科学版）》2003年第5期479-481,共3页Journal of Sichuan Normal University（Natural Science）

基　　金：南京农业大学理学院青年创新基金资助项目

摘　　要：用延拓方法研究二阶半线性椭圆型方程-Δu+f(u)=h的0 边值问题解的存在性和唯一性.首先给出方程古典解存在的一个充分必要条件和解唯一的一个充分条件,再给出解存在唯一的一个充分条件.所给的条件不同于多数文献中的形式,而是一种积分形式的整体增长控制条件.This paper is devoted to the existence and uniqueness of solution of 0boundary value problem of a class of second order semilinear elliptic equations -Δu+f(u)=h. We first present a necessary and sufficient condition for the existence of their classical solutions, and a sufficient condition for the uniqueness of the solutions. Then we give another sufficient condition for the existence and uniqueness of the solutions. These conditions controlling the growth are in integral forms, which differ from those in other literatures. The continuation method used to attack this kind of problems is one of the new points of this article.

关 键 词：半线性椭圆型方程 边值问题 解 唯一性 延拓方法 

分 类 号：O175[理学—数学]