Sign-changing solutions to a gauged nonlinear Schrödinger equation with critical exponential growth

Abstract

We study the existence and asymptotic behavior of least energy sign-changing solutions to a gauged nonlinear Schrödinger equation with critical exponential growth where are constants and Under some suitable assumptions on , we apply the constraint minimization argument to establish a least energy sign-changing solution with precisely two nodal domains. Moreover, we show that the energy of is strictly larger than two times of the ground state energy and analyze the asymptotic behavior of as . Our results generalize the existing ones, see Li G. et al. (Sign-changing solutions to a gauged nonlinear Schrödinger equation. J Math Anal Appl. 2017;455:1559–1578) and Liu Z. et al. (Existence and multiplicity of sign-changing standing waves for a gauged nonlinear Schrödinger equation in . Nonlinearity. 2019;32:3082–3111) for example, to the gauged nonlinear Schrödinger equation with critical exponential growth.