Abstract
In this paper, we study the nonlinear Choquard equation
where
is an unbounded domain,
is bounded,
, p = 2 if N = 3, 4, 5 or
if N = 3. By global compactness analysis, we show that the problem has at least one positive high energy solution.
Acknowledgements
The author would like to thank Professor Yinbin Deng very much for stimulating discussions and helpful suggestions on the present paper.
Disclosure statement
No potential conflict of interest was reported by the author(s).