Electron. J. Diff. Equ., Vol. 2013 (2013), No. 127, pp. 1-11.

Ground states for the fractional Schrodinger equation

Binhua Feng

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.

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Binhua Feng
School of Mathematics and Statistics, Lanzhou University
Lanzhou 730000, China
Tel: +86-0931-8912483; Fax: +86-0931-8912481
email: binhuaf@163.com

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