Synchronized and segregated vector solutions for nonlinear fractional Schrödinger systems

Abstract

We are concerned with the qualitative analysis of synchronized and segregated vector solutions for a class of nonlinear Schrödinger systems driven by the fractional Laplace operator. We investigate both attractive and repulsive cases. In the attractive case, we construct an unbounded sequence of non‐radial positive vector solutions whose components are synchronized, while in the repulsive case, we prove the existence of an unbounded sequence of non‐radial positive vector solutions with segregated components. A key role in the arguments developed in this paper is played by the Lyapunov‐Schmidt reduction method.