Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 127, pp. 1-11.
Title: Ground states for the fractional Schrodinger equation
Author: Binhua Feng (Lanzhou Univ., Lanzhou, China)
Abstract:
In this article, we show the existence of ground state solutions
for the nonlinear Schrodinger equation with fractional Laplacian
$$
(-\Delta )^\alpha u+ V(x)u =\lambda
|u|^{p}u\quad\hbox{in $\mathbb{R}^N$ for $\alpha \in (0,1)$}.
$$
We use the concentration compactness principle in fractional
Sobolev spaces $H^\alpha$ for $\alpha \in (0,1)$.
Our results generalize the corresponding results in the case $\alpha =1$.
Submitted November 2, 2012. Published May 27, 2013.
Math Subject Classifications: 35J60, 35Q55.
Key Words: Fractional Laplacians; nonlinear Schrodinger equation;
ground states; concentration compactness.