Existence of infinitely many high energy solutions for a class of fractional Schrödinger systems

Abstract

Abstract In this paper, we investigate a class of nonlinear fractional Schrödinger systems { ( − △ ) s u + V ( x ) u = F u ( x , u , v ) , x ∈ R N , ( − △ ) s v + V ( x ) v = F v ( x , u , v ) , x ∈ R N , $$ \left \{ \textstyle\begin{array}{l@{\quad}l}(-\triangle)^{s} u +V(x)u=F_{u}(x,u,v),& x\in \mathbb{R}^{N}, \\(-\triangle)^{s} v +V(x)v=F_{v}(x,u,v),& x\in\mathbb{R}^{N}, \end{array}\displaystyle \right . $$ where s ∈ ( 0 , 1 ) $s\in(0, 1)$ , N > 2 $N>2$ . Under relaxed assumptions on V ( x ) $V(x)$ and F ( x , u , v ) $F(x, u, v)$ , we show the existence of infinitely many high energy solutions to the above fractional Schrödinger systems by a variant fountain theorem.

Keywords

• Fractional Schrödinger system
• Variant fountain theorem
• Fractional Laplacian