A new type of solutions for a nonlinear Schrödinger system with chi ^{(2)} nonlinearities

Abstract

We are concerned with the question of constructing a new type of solution to the problem with chi ^{(2)} nonlinearities 0.1{−Δu+P(x)u=αuv,inRN,−Δv+Q(x)v=α2u2+βv2,inRN, where P(x)=P(|x|) and Q(x)=Q(|x|) are positive bounded radial potentials, 3leq N<6, alpha >0 and alpha >beta . Assuming that the potentials P(x) and Q(x) satisfy certain conditions, the existence of a new type of solutions is proved.