Sign-changing solutions for the nonlinear Chern–Simons–Schrödinger equations

Abstract

ABSTRACTIn this paper, we study the existence and asymptotic behavior of least energy sign-changing solutions for the nonlinear Chern–Simons–Schrödinger equations where , and Under suitable assumptions on f, we use some analytical skills and constraint minimization method to show that the above problem admits one least energy sign-changing solution with precisely two nodal domains. Furthermore, we show that the energy of is strictly larger than two times of the least energy, and present a convergence property of as . Finally, we also prove that the above results are valid for the Chern–Simons–Schrödinger equations with steep well potential.