拟线性椭圆型方程在无界区域上的有界解及正解

The Bounded and Positive Solutions for Quasilinear Elliptic Differential Equations in Unbounded Domains

本文主要借助上、下函数,利用局部逼近法和强极值原理,证明了 R^m 中无界区域Ω上非散度型二阶拟线性椭圆型方程 Dirichlet 问题的有界解的存在唯一性和正解的存在性,并在一定的限制下,对几种特殊情形给出了上、下函数存在的充分条件和必要条件.

In this paper,the existence and uniqueness of the bounded and posi-tive solutions of Dirichlet problems for quasilinear elliptic differentialequations of non-divergence type were proved in unbounded domains inR^m.Here we mainly used the method of super-functions and sub-functionsdealing,and a local approach.Under certain assumptions we presentedthe sufficient and the necessary conditions to exist super-functions andsub-functions.