数学物理学报 ›› 2013, Vol. 33 ›› Issue (4): 766-776.

• 论文 • 上一篇    下一篇

一类奇异椭圆型方程的多解性

彭艳芳|汪继秀   

  1. 贵州师范大学数学与计算机科学学院 贵阳 550001;襄樊学院数学与计算机学院 湖北 襄樊 441053
  • 收稿日期:2012-08-27 修回日期:2013-06-12 出版日期:2013-08-25 发布日期:2013-08-25
  • 基金资助:

    贵州省科学技术基金(黔科合J字LKS[2011]14号)资助

Multiplicity of Solutions for a Singular Equation

 PENG Yan-Fang, WANG Ji-Xiu   

  1. School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001; School of Mathematics and Computer Science, Xiangfan University, Hubei |Xiangfan 441053
  • Received:2012-08-27 Revised:2013-06-12 Online:2013-08-25 Published:2013-08-25
  • Supported by:

    贵州省科学技术基金(黔科合J字LKS[2011]14号)资助

摘要:

考虑了下面一类奇异椭圆型方程
 div(|x|-2au)-μ u/|x|2(1+a)=up-1/|x|bp+λ uq-1/|x|dD.
 利用Ekeland 变分原理及山路引理, 证明了在参数μλ满足一定条件下, 方程存在多个正解.

关键词: 正解, Ekeland 变分原理, 奇异性, Caffarelli-Kohn-Nirenberg 不等式

Abstract:

In this paper, we consider a singular elliptic equation
div(|x|-2au)-μ u/|x|2(1+a)=up-1/|x|bp+λ uq-1/|x|dD.
By virtue of Ekeland variational principle and Mountain  Pass lemma, we prove the equation have multiple positive solutions with a range of the parameters μ and λ.

Key words: Positive solutions, Ekeland , variational principle, Singularity, Caffarelli-Kohn-Nirenberg inequality

中图分类号: 

  • 35J25