Existence of solutions for singularly perturbed Schrödinger equations with nonlocal part

In the present paper we study the existence of solutions for a nonlocal Schrödinger equation{eqnarray*} -ε^2Δ u +V(x)u =(∫R^3 {|u|ᵖ}{|x-y|μ}dy)|u|ᵖ⁻²u,{eqnarray*}where 0 < μ < 3 and 6-μ/3 < p < 6-μ. Under suitable assumptions on the potential $V(x)$, if the parameter ε is small enough, we prove the existence of solutions by using Mountain-Pass Theorem.