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

@article{Benmouloud2016ARB,
  title={A refined bound on the dimension of ℝ N for an elliptic system involving critical terms with infinitely many solutions},
  author={Samira Benmouloud and Mustapha Khiddi and Simohammed Sba{\"i}},
  journal={Advances in Nonlinear Analysis},
  year={2016},
  volume={7},
  pages={85 - 96}
}
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 ≥ 7 to N > max(4, ⌊2s⌋ + 2), where 0 < s < 2 and still end up with… CONTINUE READING

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