Abstract:

In this article, the authors consider the existence of a nontrivial solution
for the following equation:
-△ u + u =q(x)(|u|²*{1/|x|})u, x∈ R³,
where q(x) satisfies some conditions. Using a Min-Max method, the authors prove that there is at least one nontrivial solution for the above equation.

Key words: Existence, Choquard's equation, Min-Max