On standing waves with a vortex point of order N for the nonlinear Chern–Simons–Schrödinger equations

In this paper, we are interested in standing waves with a vortex for the nonlinear Chern–Simons–Schrödinger equations (CSS for short). We study the existence and the nonexistence of standing waves when a constant λ>0, representing the strength of the interaction potential, varies. We prove every standing wave is trivial if λ∈(0,1), every standing wave is gauge equivalent to a solution of the first order self-dual system of CSS if λ=1 and for...