Asymptotically periodic quasilinear Schrödinger equations with critical exponential growth

Abstract

In this work, we study the existence of a positive solution for a class of quasilinear Schrödinger equations involving a potential that behaves like a periodic function at infinity and the nonlinear term may exhibit critical exponential growth. In order to prove our main result, we combine minimax methods with a version of the Trudinger–Moser inequality. These equations appear naturally in mathematical physics and have been derived as models of several physical phenomena.