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

Samira Benmouloud, Mustapha Khiddi, Simohammed Sbaï
2018 Advances in Nonlinear Analysis  
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)} 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\geq 7} to {N>\max(4,\lfloor 2s\rfloor+2)} , where {0<s<2} and still end up with infinitely many solutions.
doi:10.1515/anona-2015-0164 fatcat:qh46hijazrhk7dx3vk7grmzdiq