数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (2): 423-438.doi: 10.1016/S0252-9602(15)60013-3

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SOLUTIONS TO ELLIPTIC SYSTEMS INVOLVING DOUBLY CRITICAL NONLINEARITIES AND HARDY-TYPE POTENTIALS

康东升, 罗婧, 史晓琳   

  1. School of Mathematics and Statistics, South-Central University for Nationalities, Wuhan 430074, China
  • 收稿日期:2013-09-20 出版日期:2015-03-20 发布日期:2015-03-20
  • 基金资助:

    This work is supported by the Science Foundation of State Ethnic Affairs Commission of the People's Republic of China (12ZNZ004).

SOLUTIONS TO ELLIPTIC SYSTEMS INVOLVING DOUBLY CRITICAL NONLINEARITIES AND HARDY-TYPE POTENTIALS

Dongsheng KANG, Jing LUO, Xiaolin SHI   

  1. School of Mathematics and Statistics, South-Central University for Nationalities, Wuhan 430074, China
  • Received:2013-09-20 Online:2015-03-20 Published:2015-03-20
  • Supported by:

    This work is supported by the Science Foundation of State Ethnic Affairs Commission of the People's Republic of China (12ZNZ004).

摘要:

In this article, an elliptic system is investigated, which involves Hardy-type po- tentials, critical Sobolev-type nonlinearities, and critical Hardy-Sobolev-type nonlinearities. By a variational global-compactness argument, the Palais-Smale sequences of related approx- imation problems is analyzed and the existence of infinitely many solutions to the system is established.

关键词: Elliptic system, solution, critical nonlinearity, Hardy inequality, global com- pactness

Abstract:

In this article, an elliptic system is investigated, which involves Hardy-type po- tentials, critical Sobolev-type nonlinearities, and critical Hardy-Sobolev-type nonlinearities. By a variational global-compactness argument, the Palais-Smale sequences of related approx- imation problems is analyzed and the existence of infinitely many solutions to the system is established.

Key words: Elliptic system, solution, critical nonlinearity, Hardy inequality, global com- pactness

中图分类号: 

  • 35J50