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关于二阶半线性椭圆方程的Dirichlet边值问题一个注记
敖恩^1,2, 张国伟¹
1.东北大学数学系, 辽宁沈阳 110819;2.赤峰学院数学与统计学院, 内蒙古赤峰 024000

摘要:

本文研究二阶半线性椭圆方程的Dirichlet边值问题.利用山路引理和最小作用原理,获得了在新条件下具有Dirichlet边值问题的二阶半线性椭圆方程的弱解的存在性的结果.

关键词: 椭圆方程山路引理最小作用原理临界点

DOI：

分类号:O175.25;O175.8

基金项目:Supported by National Natural Science Foundation of China (10971179).

A NOTE ON DIRICHLET PROBLEM FOR SEMILINEAR SECOND ORDER ELLIPTIC EQUATION

AO En^1,2, ZHANG Guo-wei¹

1.Department of Mathematics, Northeastern University, Shenyang 110819, China;2.School of Mathematics and Statistics, Chifeng University, Chifeng 024000, China

Abstract:

In this paper, we study the Dirichlet problem for semilinear second order elliptic equation. By using the mountain pass lemma and the least action principle, we obtain the existence of weak solution to semilinear second order elliptic equation under some new conditions which are different from the previous ones.

Key words: elliptic equation mountain pass lemma least action principle critical point