Existence and concentration of solutions for a fractional Schrodinger equations with sublinear nonlinearity

Abstract

This article concerns the fractional elliptic equations \begin{equation*}(-Δ)^{s}u+λV(x)u=f(u), \quad u\in H^{s}(\mathbb{R}^N), \end{equation*}where $(-\Delta {)}^s$ ($s\in (0,1)$) denotes the fractional Laplacian, $\lambda >0$ is a parameter, $V\in C({\mathbb{R}}^N)$ and $V^{-1}(0)$ has nonempty interior. Under some mild assumptions, we establish the existence of nontrivial solutions. Moreover, the concentration of solutions is also explored on the set $V^{-1}(0)$ as $\lambda \to \infty$.

8pages

References in corpus (1)

• Positive solutions to some asymptotically linear fractional Schrodinger equations