### Nonlocal Schrödinger equations for integro-differential operators with measurable kernels

DOI: http://dx.doi.org/10.12775/TMNA.2019.056

#### 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.

#### Keywords

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