## Rocky Mountain Journal of Mathematics

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

### Multiplicity results for a fractional Schrodinger equation with potentials

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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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Mathematical Reviews (MathSciNet): MR2152503

Zentralblatt MATH: 1081.49002

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