arXiv subjects

Sofiane Khoutir

Publications and source records attributed to Sofiane Khoutir.

2 recordsLinked to original sources

arXiv2021

Multiple solutions for a fractional Schrodinger equation with potentials

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 $s\in (0,1)$, $\ N>2s$, $(-Δ)^{s}$ 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 $u$.

math.AP↗

arXiv2020

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

This paper is devoted to the following class of nonlinear fractional Schrödinger equations: \begin{equation*} (-Δ)^{s} u + V(x)u = f(x,u) + λg(x,u), \quad \text{in}\: \mathbb{R}^N, \end{equation*} where $s\in (0,1)$, $N>2s$, $(-Δ)^{s}$ stands for the fractional Laplacian, $λ\in \mathbb{R}$ is a parameter, $V\in C(\mathbb{R}^N,R)$, $f(x,u)$ is superlinear and $g(x,u)$ is sublinear with respect to $u$, respectively. We prove the existence of infinitely many high energy solutions of the aforementioned equation by means of the Fountain theorem. Some recent results are extended and sharply improved.

math.AP↗