Nonlocal Schrödinger equations for integro-differential operators with measurable kernels

Abstract

In this paper we investigate the existence of positive solutions for the problem $$ -\mathcal{L}_{K}u+V(x)u=f(u) $$% in $\mathbb R^N$, where $-\mathcal{L}_{K}$ is an integro-differential operator with measurable kernel $K$. Under apropriate hypotheses, we prove by variational methods that this equation has a nonnegative solution.