Existence of a nontrivial solution for a strongly indefinite periodic Schrodinger-Poisson system
Shaowei Chen, Liqian Xiao · arXiv (Cornell University) · 2014
We consider the Schrödinger-Poisson system \begin{eqnarray}\left\{\begin{array} [c]{ll} -Δu+V(x) u+|u|^{p-2}u=λϕu, & \mbox{in}\mathbb{R}^{3},\\ -Δϕ= u^{2}, & \mbox{in}\mathbb{R}^{3}. \end{array} \right. onumber \end{eqnarray} where $λ>0$ is a parameter, $30,$ this system has a nontrivial solution.