Nodal standing waves for a gauged nonlinear Schrödinger equation in R2

This paper investigates the existence and asymptotic behavior of nodal solutions to the following gauged nonlinear Schrödinger equation{−Δu+ωu+(h2(|x|)|x|2+∫|x|+∞h(s)su2(s)ds)u=λ|u|p−2u,x∈R2,u(x)=u(|x|)∈H1(R2), where ω,λ>0, p>6 andh(s)=12∫0sru2(r)dr is the so-called Chern-Simons term. We prove that for any positive integer k, the problem has a sign-changing solution uλk which changes sign exactly k times. Moreover, the energy of ukλ is strictly increasing in k, and for any sequence {λn}→+∞(n→∞), there exists a subsequence {λns}, such that (λns)1p−2ukλns converges in H1(R2) to wk as s→∞, where wk also changes sign exactly k times and solves the following equation−Δu+ωu=|u|p−2u,u∈H1(R2).