Electron. J. Diff. Equ., Vol. 2015 (2015), No. 25, pp. 1-11.

Multiple solutions for fractional Schrodinger equations

Hongxia Shi, Haibo Chen

Abstract:
In this article we study the fractional Schr\"odinger equations
$$
 (-\Delta)^{\alpha}u+V(x)u=f(x,u)  \quad\text{in }\mathbb{R}^{N},
 $$
where $0<\alpha<1$, $N\geq2$, $(-\Delta)^{\alpha}$ stands for the fractional Laplacian of order $\alpha$. First by using Morse theory in combination with local linking arguments, we prove the existence of at least two nontrivial solutions. Next we prove that the problem has k distinct pairs of solutions by using the Clark theorem.

Submitted November 16, 2014. Published January 27, 2015.
Math Subject Classifications: 35B38, 35G99.
Key Words: Fractional Schrodinger equations; variational methods; Morse theory; local linking.

Show me the PDF file (244 KB), TEX file, and other files for this article.

Hongxia Shi
School of Mathematics and Statistics
Central South University
Changsha, 410083 Hunan, China
email: shihongxia5617@163.com
Haibo Chen
School of Mathematics and Statistics
Central South University
Changsha, 410083 Hunan, China
email: math_chb@163.com

Return to the EJDE web page