LAUSR

In this paper we investigate the existence of infinitely many solutions for nonlocal Schrödinger equation involving a magnetic potential (−△)Asu+V(x)u=f(x,|u|)u,in RN,$$ (-\triangle )_{A}^{s}u+V(x)u=f\bigl(x, \vert u \vert \bigr)u, \quad\text{in } {\mathbb {R}}^{N}, $$ where s∈(0,1)$s\in (0,1)$ is fixed, N>2s$N>2s$, V:RN→R+$V:{\mathbb {R}}^{N}\rightarrow {\mathbb {R}}^{+}$ is an electric potential, the magnetic potential A:RN→RN$A:{\mathbb {R}}^{N}\rightarrow {\mathbb {R}}^{N}$ is a continuous function, and (−△)As$(-\triangle )_{A}^{s}$ is the fractional magnetic operator. Under suitable assumptions for the potential function V and nonlinearity f, we obtain the existence of infinitely many nontrivial high energy solutions by using the variant fountain theorem.