New synchronized solutions for linearly coupled Schrödinger systems

Abstract

In this paper, we consider the following linearly coupled Schrödinger system:(Pε){−Δu+P(|y|)u=u3+λ(|y|)vinR3,−Δv+Q(|y|)v=v3+λ(|y|)uinR3, where P(|y|), Q(|y|) and λ(|y|) are positive radial potentials such that λ(|y|)<min⁡{P(|y|),Q(|y|)}. Motivated by the work of Duan and Musso [9], we use the Lyapunov–Schmidt reduction method to construct new synchronized solutions of the problem (Pε) with more complex concentration structure than the results in Wei, Yan [26] and Peng, Wang [23], when P(|y|), Q(|y|) and λ(|y|) satisfy some decay assumptions at infinity.