数学物理学报 ›› 2013, Vol. 33 ›› Issue (6): 1099-1111.

• 论文 • 上一篇    下一篇

一类非齐次临界椭圆方程在RN中的正解

谢华朝|李素丽   

  1. 河南财经政法大学 数学与信息科学系 郑州 450002
  • 收稿日期:2012-05-22 修回日期:2013-06-06 出版日期:2013-12-25 发布日期:2013-12-25
  • 基金资助:

    河南省自然科学基金(12B110002)资助

Positive Solutions for An Inhomogeneous Singular Elliptic Equation with Critical Exponent in RN

 XIE Hua-Chao, LI Su-Li   

  1. Department of Mathematics, Henan University of Economics and Law, Zhengzhou 450002
  • Received:2012-05-22 Revised:2013-06-06 Online:2013-12-25 Published:2013-12-25
  • Supported by:

    河南省自然科学基金(12B110002)资助

摘要:

研究了一类带奇异项的非齐次半线性椭圆方程. 利用变分方法, 该文讨论了其正解的存在性和不存在性, 以及解的唯一性和多解性.

关键词: 非齐次椭圆方程, 临界指数, Hardy 项, 正解

Abstract:

A semilinear elliptic problem with singular coefficient and inhomogeneous term is mainly studied. The existence and nonexistence of solutions for the inhomogeneous elliptic equation are proved by variational methods and  analytic technique. Meanwhile, multiplicity  and uniqueness of solutions are also investigated.

Key words: Inhomogeneous elliptic equation, Critical exponent, Hardy term, Positive solutions

中图分类号: 

  • 35J60