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In this paper, we investigate the existence of nonnegative solutions for theproblem $$ -\mathcal{L}_{K}u+V(x)u=f(u) $$ in $\mathbb R^n$, where$-\mathcal{L}_{K}$ is a integro-differential operator with measurable kernel$K$ and $V$ is a continuous potential. Under apropriate hypothesis, we prove,using variational methods, that the above equation has solution.

Nonlocal Schrodinger Equations for Integro-Differential Operators with Measurable Kernels and Asymptotic Potentials