Mountain-pass type solutions for the Chern-Simons-Schrödinger equation with critical exponential growth

Abstract

In this paper, we consider the nonlinear Chern-Simons-Schrödinger equations where is the so-called Chern-Simons term, has critical exponential growth which behaves like . By combing the variational methods, Trudinger-Moser inequality and some new approaches to estimate precisely the minimax level of the energy functional, we prove the existence of a mountain-pass type solution for the above problem under some weak assumptions. Our results improve and extend the previous results.