Nonlocal Schrodinger Equations for Integro-Differential Operators with   Measurable Kernels and Asymptotic Potentials
  In this paper, we investigate the existence of nonnegative solutions for the problem $$ -\mathcal{L}_{K}u+V(x)u=f(u) $$ in $\mathbb R^n$, where $-\mathcal{L}_{K}$ 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. 
Ronaldo C. Duarte and Marco A. S. Souto
math.AP