Speaker: Researcher Xuexiu Zhong（South China Normal University）

Title: Normalized solutions for a coupled Schrodinger system

Time: Fri Nov.1, 2019,PM:3:00-4:30

Location: Room 4318, Building No.4, Wushan Campus

Abstract：

    In this talk, we focus on a class of systems of coupled Schrödinger equations, satisfying the normalization constraints on the masses of the two components. The standard approach to this problem is variational with frequencies appearing as Lagrange multipliers. Here we present a new approach based on bifurcation theory and the continuation method. We obtain the existence of normalized solutions for any given masses for the couple constant in a large range. We also give a result about the nonexistence of positive solutions. From which one can see that our existence theorem is almost the best. Especially, if the intraspecies scattering lengths equal, we prove that normalized solutions exist for all positive interspecies scattering length and all masses. We also state and discuss some new non-existence and uniqueness theorems for the problem that will enter in the proofs of our results on normalized solutions, which have some interest in itself.