Existence and Concentration of Solutions for a Nonlinear Choquard Equation

In this paper, we consider the nonlinear Choquard equation - Δ u + ( 1 + μ g ( x ) ) u = ( K α ( x ) ∗ | u | p ) | u | p - 2 u , x ∈ R N , where N ≥ 3 , α ∈ ( 0 , N ) , p ∈ ( N + α N , N + α N - 2 ) , μ > 0 is a parameter, K α ( x ) is the Riesz potential and g ( x ) is a nonnegative continuous potential. Under some assumptions on g ( x ), we obtain the existence of ground state solutions and concentration results by using the critical point theory.