Multiple positive solutions for Schrödinger systems with mixed couplings

Abstract

We study the effects of mixed couplings for nonlinear Schrodinger systems. We show due to the mixed couplings there exist multiple vector positive solutions which exhibit interesting new patterns of co-existence of synchronization and segregation. For a 3-system we show the existence of multiple positive vector solutions with the first two components being synchronized and segregated from the third component. We investigate the asymptotic of these solutions with a large attractive coupling constant.