Rocky Mountain Journal of Mathematics

Multiplicity results for a fractional Schrodinger equation with potentials

Sofiane Khoutir

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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 $u$.

Article information

Source
Rocky Mountain J. Math., Volume 49, Number 7 (2019), 2205-2226.

Dates
First available in Project Euclid: 8 December 2019

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1575774134

Digital Object Identifier
doi:10.1216/RMJ-2019-49-7-2205

Mathematical Reviews number (MathSciNet)
MR4039966

Zentralblatt MATH identifier
07152861

Subjects
Primary: 35J20: Variational methods for second-order elliptic equations 35J60: Nonlinear elliptic equations

Keywords
Fractional Schrodinger equation sublinear variational methods Moser iteration method

Citation

Khoutir, Sofiane. Multiplicity results for a fractional Schrodinger equation with potentials. Rocky Mountain J. Math. 49 (2019), no. 7, 2205--2226. doi:10.1216/RMJ-2019-49-7-2205. https://projecteuclid.org/euclid.rmjm/1575774134


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