Electron. J. Diff. Equ., Vol. 2015 (2015), No. 223, pp. 1-16.

Ground state solutions for non-local fractional Schrodinger equations

Yang Pu, Jiu Liu, Chun-Lei Tang

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.

Submitted June 15, 2015. Published August 28, 2015.
Math Subject Classifications: 35J60, 35J20
Key Words: Nonlinear Schrodinger equation; fractional Laplacian; non-local operator; ground state solution.

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Yang Pu
School of Mathematics and Statistics
Southwest University
Chongqing 400715, China
email: pt8820@swu.edu.cn
Jiu Liu
School of Mathematics and Statistics
Southwest University
Chongqing 400715, China
email: jiuliu2011@163.com
Chun-Lei Tang
School of Mathematics and Statistics
Southwest University
Chongqing 400715, China
Phone +86 23 68253135, fax +86 23 68253135
email: tangcl@swu.edu.cn

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