The sign-changing solutions and ground states for planar Schrödinger–Newton system with an exponential critical growth

Abstract

In this paper, we study the planar Schrödinger–Newton system with a Coulomb potential where the nonlinearity is super-linear at zero and exponential critical at infinity. With a weaker condition than the Nehari type monotonic condition, we obtain a least-energy sign-changing solution via the variational method. Moreover, we obtain the existence of ground states, and the energy of any nodal solution is strictly larger than two times the least energy. We also give some convergence properties of the ground states.