半线性二阶椭圆型方程组正解的对称性和单调性

本文讨论了如下半线性二阶椭圆型方程组边值问题正解的对称性和单调性,简化了文献4]中主要结果的证明,且将其推广于一般的有界单连通凸区域.最后,给出了一些实际应用的例子,证明所用的主要工具是窄小区域上的极值原理和平移平面法。

MONOTONICITY AND SYMMETRY OF PARTIALLINEAR SECOND-ORDER ELLIPTICALEQUATIONS'POSITIVE SOLUTION

The method of moving planes and an improved forms of the Maximum Principle in"Narrow domains"are used in proving monotonicity and symmetry in a bounded domain which is convex. Here,we present a much simplified approach to these methods. At the same time,it yields improved results. Finally,by using the results above,we get same useful con-clutions of some example in reality.