The existence of ground state normalized solutions for Chern-Simons-Schrödinger systems

Abstract

In this paper, we study normalized solutions of the Chern-Simons-Schrödinger system with general nonlinearity and a potential in H¹(ℝ)². When the nonlinearity satisfies some general 3-superlinear conditions, we obtain the existence of ground state normalized solutions by using the minimax procedure proposed by Jeanjean in [L. Jeanjean, Existence of solutions with prescribed norm for semilinear elliptic equations, Nonlinear Anal. (1997)].