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math.AP2014
Nontrivial solutions for periodic Schrödinger equations with sign-changing nonlinearities
Shaowei Chen, Conglei Wang, Liqin Xiao
Using a new infinite-dimensional linking theorem, we obtained nontrivial solutions for strongly indefinite periodic Schrödinger equations with sign-changing nonlinearities.
math.AP2014
Existence of nontrivial solutions for periodic Schrodinger equations with new nonlinearities
Shaowei Chen, Dawei Zhang
We study the Schrödinger equation: \begin{eqnarray} - Δu+V(x)u+f(x,u)=0,\qquad u\in H^{1}(\mathbb{R}^{N}),\nonumber \end{eqnarray} where is periodic and is periodic in the…
math.AP2014
Existence of a nontrivial solution for a strongly indefinite periodic Schrodinger-Poisson system
Shaowei Chen, Liqian Xiao
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…