Choquard Equations with Mixed Potential

In this paper, we study the following class of nonlinear Choquard equation, $-Δu+a(z)u=K(u)f(u)\quad \text{in}\quad \R^N,$ where $\R^N=\R^L\times\R^M$, $L\geq2$, $K(u)=|.|^{-γ}*F(u)$, $γ\in(0,N)$, $a$ is a continuous real function and $F$ is the primitive function of $f$. Under some suitable assumptions mixed on the potential $a$. We prove existence of a nontrivial solution for the above equation.

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