数学物理学报 ›› 2012, Vol. 32 ›› Issue (5): 833-839.

• 论文 • 上一篇    下一篇

一类特殊半线性椭圆型方程的多解问题

张正杰|余小玲   

  1. 华中师范大学数学与统计学院 武汉 430079
  • 收稿日期:2011-09-18 修回日期:2012-04-17 出版日期:2012-10-25 发布日期:2012-10-25
  • 基金资助:

    国家自然科学基金和数学物理湖北省重点实验室(华中师范大学)资助

Multiple Solutions for a kind of Special Semilinear Elliptic Equations

 ZHANG Zheng-Jie, YU Xiao-Ling   

  1. School of Mathematics and Statistics Central China Normal University, Wuhan 430079
  • Received:2011-09-18 Revised:2012-04-17 Online:2012-10-25 Published:2012-10-25
  • Supported by:

    国家自然科学基金和数学物理湖北省重点实验室(华中师范大学)资助

摘要:

研究如下一类半线性椭圆型方程
     {-Δu=(1+εg(x))(u-1)p+,        x∈RN,
        uD1,2(RN),          u(x)→0 ,        |x|→∞,

 这里ε是正常数, g(x)∈L(RN), 1<p<N+2/N-2. 应用扰动方法证明了: g(x)适合一定条件, 则存在ε0, 只要0<ε<ε0, 上述问题存在多个解.

关键词: 半线性, 椭圆型, 多解

Abstract:

In this paper, we consider the following problem
         {-Δu=(1+εg(x))(u-1)p+,        x∈RN,
        uD1,2(RN),          u(x)→0 ,        |x|→∞,

where ε is a positive constant, g(x)∈L(RN), 1<p<N+2/N-2. Used perturbation method, we prove that under some conditions on g(x), there exists a ε0, if 0<ε<ε0, such that there are many solutions for above problem.

Key words: Semilinear, Elliptic, Multiple solutions

中图分类号: 

  • 35J60