Number of synchronized solutions for linearly coupled elliptic systems

Abstract: In this talk, we use the Lyapunov-Schmidt reduction method to construct a solution with multiple spikes for a class of singularly perturbed Schrödinger systems with linearly coupled terms. Via blow up

method, we give an upper bound for the number of spikes. Thus by changing the number of spikes, we obtain the optimal number of synchronized solutions for these systems.