Multiple mixed interior and boundary peaks synchronized solutions for nonlinear coupled elliptic systems

Abstract

This paper is devoted to a class of singularly perturbed nonlinear Schrödinger systems defined on a smooth bounded domain in RN(N=2,3). We use the Lyapunov–Schmidt reduction method to construct synchronized vector solutions with multiple spikes both on the boundary and in the interior of the domain. For each vector solution that has been constructed, we point out that the interior spikes locate near sphere packing points in the domain, and the boundary spikes locate near the critical points of the mean curvature function related to the boundary of the domain.