Multiple solutions for a fractional Schrodinger equation with potentials

Abstract

This paper is devoted to study a class of nonlinear fractional Schrödinger equations: \begin{equation*} (-Δ)^{s}u+V(x)u=f(x,u), \quad \text{in}\: \mathbb{R}^{N}, \end{equation*} where $s\in (0,1)$, $N>2s$, $(-\Delta {)}^s$ stands for the fractional Laplacian. First, 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 $f(x,u)$. Next, 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 $u$.

References in corpus (3)

• Multiplicity and concentration results for some nonlinear Schrödinger equations with the fractional $p$-Laplacian
• Sign-changing solutions for a class of zero mass nonlocal Schrödinger equations
• Multiple solutions for a class of nonhomogeneous fractional Schrödinger equations in ${\mathbb{R}}^N$

Cited by in corpus (1)

• Existence of infinitely many solutions for a class of fractional Schrödinger equations in ${\mathbb{R}}^N$ with combined nonlinearities