Ground state solutions for non-local fractional Schrodinger equations

Abstract

In this article, we study a time-independent fractional Schrodinger equation with non-local (regional) diffusion $$ (-\Delta)^{\alpha}_{\rho}u + V(x)u = f(x,u) \quad \text{in }\mathbb{R}^{N}, $$ where $\alpha \in (0,1)$, $N > 2\alpha$. We establish the existence of a non-negative ground state solution by variational methods.

Keywords

• Nonlinear Schrodinger equation
• fractional Laplacian
• non-local operator
• ground state solution