Positive and sign-changing solutions for the nonlinear Schrödinger systems with synchronization and separation

Qingfang Wang, Wenju Wu

In this paper, we consider the following nonlinear Schrödinger system: -$\Delta$ u+P(x)u=${\mu }_1$ $u^3$+$\beta$ u$v^2$, x $\in$ $R^3$,\\ -$\Delta$ v+Q(x)v=${\mu }_2$ $v^3$+$\beta$ $u^2$v, x $\in$ $R^3$, whe…