Chern-Simons limit of ground state solutions for the Schrödinger equations coupled with a neutral scalar field

Abstract

We consider a class of the Schrödinger equation coupled with an neutral scalar field in non-radial symmetric space H1(R2). In this paper, combining the Nehari manifold, Moser iteration and some analytical skills, we get a positive ground state solution to the problem, which is classical and spherically symmetric. At the same time, this solution together with its derivatives up to order 2 has exponential decay at infinity. Moreover, the asymptotic behavior of solutions is analyzed under the sense of Chern-Simons limit. Our work can be regarded as a supplement and extension to Han et al. (2014) [12], where they rely heavily on the symmetry of work space.