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.
Acknowledgments
The author would like to express his sincere and warmest thanks to the anonymous referees for carefully reading the manuscript and valuable comments and suggestions.
Disclosure statement
No potential conflict of interest was reported by the author(s).