A refined bound on the dimension of ℝ N for an elliptic system involving critical terms with infinitely many solutions

Advances in Nonlinear Analysis

article

Samira Benmouloud¹  Mustapha Khiddi¹  Simohammed Sbaï¹ 

[1] Fac. Sciences, Université Ibn Tofail

关键词: Elliptic system;    infinitely many solutions;    critical exponent;    variational method;   

DOI  :  10.1515/anona-2015-0164

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

In this paper, we extend the result of Yan and Yang [16] on equations to an elliptic system involving critical Sobolev and Hardy–Sobolev exponents in bounded domains satisfying some geometric condition. In addition, we weaken the conditions on the dimension N and on the potential a⁢(x){a(x)} set in [16]. Our main result asserts, by a variational global-compactness argument, that the condition on the dimension N can be refined from N≥7{N\geq 7} to N>max⁡(4,⌊2⁢s⌋+2){N>\max(4,\lfloor 2s\rfloor+2)}, where 0

【 授权许可】

CC BY