Nonlocal Schrödinger equations for integro-differential operators with measurable kernels

Ronaldo C. Duarte, Marco A. S. Souto

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


Integro-differential operator; nonlocal Schrödinger equation; asymptotic potential

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