Translator Disclaimer
2019 Multiplicity results for a fractional Schrodinger equation with potentials
Sofiane Khoutir
Rocky Mountain J. Math. 49(7): 2205-2226 (2019). DOI: 10.1216/RMJ-2019-49-7-2205

Abstract

We study a class of nonlinear fractional Schrodinger equations: \[ (-\Delta )^{s}u+V(x)u=f(x,u) \text { in } \mathbb{R} ^{N}, \] where $s\in (0,1)$, $N>2s$, $(-\Delta )^{s}$ stands for the fractional Laplacian. By using a variational approach, we establish the existence of at least one nontrivial solution for the above equation with a general potential $V(x)$ which is allowed to be sign-changing and a sublinear nonlinearity $f(x,u)$. Moreover, by using variational methods and the Moser iteration technique, we prove the existence of infinitely many solutions with $V(x)$ is a nonnegative potential and the nonlinearity $f(x,u)$ is locally sublinear with respect to $u$.

Citation

Download Citation

Sofiane Khoutir. "Multiplicity results for a fractional Schrodinger equation with potentials." Rocky Mountain J. Math. 49 (7) 2205 - 2226, 2019. https://doi.org/10.1216/RMJ-2019-49-7-2205

Information

Published: 2019
First available in Project Euclid: 8 December 2019

zbMATH: 07152861
MathSciNet: MR4039966
Digital Object Identifier: 10.1216/RMJ-2019-49-7-2205

Subjects:
Primary: 35J20, 35J60

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
22 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.49 • No. 7 • 2019
Back to Top