## Topological Methods in Nonlinear Analysis

### 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.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 54, Number 1 (2019), 383-406.

Dates
First available in Project Euclid: 22 July 2019

https://projecteuclid.org/euclid.tmna/1563760821

Digital Object Identifier
doi:10.12775/TMNA.2019.056

#### Citation

Duarte, Ronaldo C.; Souto, Marco A. S. Nonlocal Schrödinger equations for integro-differential operators with measurable kernels. Topol. Methods Nonlinear Anal. 54 (2019), no. 1, 383--406. doi:10.12775/TMNA.2019.056. https://projecteuclid.org/euclid.tmna/1563760821

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