Sign-changing solutions to a gauged nonlinear Schrödinger equation with critical exponential growth. Issue 5 (4th May 2022) - Shen, Liejun
Abstract : We study the existence and asymptotic behavior of least energy sign-changing solutions to a gauged nonlinear Schrödinger equation with critical exponential growth 1 − Δ u + ω u + λ h 2 ( | x | ) | x | 2 + ∫ | x | ∞ h ( s ) s u 2 ( s ) d s u = f ( u ) i n     R 2, u ∈ H r 1 ( R 2 ), where ω, λ > 0 are constants and 2 h ( s ) = ∫ 0 s r 2 u 2 ( r ) d r . Under some suitable assumptions on f ∈ C ( R ), we apply the constraint minimization argument to establish a least energy sign-changing solution u λ with precisely two nodal domains. Moreover, we show that the energy of u λ is strictly larger than two times of the ground state energy and analyze the asymptotic behavior of u λ as λ ↘ 0 + . 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 R 2 . Nonlinearity. 2019;32:3082–3111) for example, to the gauged nonlinear Schrödinger equation with critical exponential growth.