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

2016/12/17 by Duarte, Ronaldo C., Souto, Marco A. S.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1612.05696

Abstract

In this paper, we investigate the existence of nonnegative solutions for the problem -L_Ku+V(x)u=f(u) in \mathbb Rⁿ, where -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.

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