Existence of solutions to a class of quasilinear Schr?dinger systems involving the fractional $p$-Laplacian

摘要

The purpose of this paper is to investigate the existence of solutions to the following quasilinear Schr"{o}dinger type system driven by the fractional $p$-Laplacian egin{align*} (-Delta)^{s}_pu+a(x)|u|^{p-2}u&=H_u(x,u,v)quad mbox{in } mathbb{R}^N, (-Delta)^s_qv+b(x)|v|^{q-2}v&=H_v(x,u,v)quad mbox{in } mathbb{R}^N, end{align*} where $1