Infinitely Many Solutions for a Fractional Schrödinger Equation in $$\mathbb {R}^N$$ with Combined Nonlinearities

Abstract

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