数学物理学报(英文版) ›› 2004, Vol. 24 ›› Issue (4): 639-644.

• 论文 • 上一篇    下一篇

EXISTENCE OF POSITIVE SOLUTIONS TO QUASI-LINEAR EQUATION INVOLVING CRITICAL SOBOLEV-HARDY EXPONENT

 康东升   

  1. Department of Mathematics, South-Central University For Nationalitis, Wuhan 430074, China
  • 出版日期:2004-10-20 发布日期:2004-10-20
  • 基金资助:

    This research is supported by the National Natural Science Foundation of China(10171036) and the Natural Science Foundation of South-Central University For Nationalities(YZZ03001).

EXISTENCE OF POSITIVE SOLUTIONS TO QUASI-LINEAR EQUATION INVOLVING CRITICAL SOBOLEV-HARDY EXPONENT

 KANG Dong-Sheng   

  1. Department of Mathematics, South-Central University For Nationalitis, Wuhan 430074, China
  • Online:2004-10-20 Published:2004-10-20
  • Supported by:

    This research is supported by the National Natural Science Foundation of China(10171036) and the Natural Science Foundation of South-Central University For Nationalities(YZZ03001).

摘要:

This paper is concerned with the quasi-linear equation with critical Sobolev-Hardy exponent −pu =|u|p∗(s)−2|x|su + |u|r−2u + μ|u|q−2|x|tu in ,u = 0 on @,where   RN(N  3) is a smooth bounded domain, 0 2 , 0  s < p, 1 < p < N, p(s) :=p(N−s)N−p is the critical Sobolev-Hardy exponent,  > 0, p  r < p, p := Np N−p is the critical Sobolev exponent, μ > 0, 0  t < p, p  q < p(t) = p(N−t)N−p . The existence of a positive solution is proved by Sobolev-Hardy inequality and variational method.

关键词: Positive solution, quasi-linear equation, critical Sobolev-Hardy exponent,variational method

Abstract:

This paper is concerned with the quasi-linear equation with critical Sobolev-Hardy exponent −pu =|u|p∗(s)−2|x|su + |u|r−2u + μ|u|q−2|x|tu in ,u = 0 on @,where   RN(N  3) is a smooth bounded domain, 0 2 , 0  s < p, 1 < p < N, p(s) :=p(N−s)N−p is the critical Sobolev-Hardy exponent,  > 0, p  r < p, p := Np N−p is the critical Sobolev exponent, μ > 0, 0  t < p, p  q < p(t) = p(N−t)N−p . The existence of a positive solution is proved by Sobolev-Hardy inequality and variational method.

Key words: Positive solution, quasi-linear equation, critical Sobolev-Hardy exponent,variational method

中图分类号: 

  • 35J25