Multiple solutions for a nonlinear Schrödinger systems
Multiple solutions for a nonlinear Schrödinger systems
This paper is concerned with the following nonlinear Schrödinger systems: \begin{document}$ \left\{\begin{aligned}-\Delta u+a(x)u& = |u|^{p-2}u+\beta |u|^{\frac{p}{2}-2}u|v|^{\frac{p}{2}} \ \ \hbox{in } \mathbb{R}^{N}\\-\Delta v+a(x)v& = |v|^{p-2}v+\beta |v|^{\frac{p}{2}-2}v|u|^{\frac{p}{2}}\ \ \ \hbox{in } \mathbb{R}^{N}\\(u,v)&\in (H^1(\mathbb{R}^N))^2,\end{aligned}\right. \ \ \ \ \ \ \ {(P)} $\end{document} where $ N\geq3 $ and $ 2<p<\frac{2N}{N-2} = 2^{\ast} $, …