A multiplicity result for Chern-Simons-Schrödinger equation with a general nonlinearity

Abstract

In this paper we give a multiplicity result for the following Chern-Simons-Schrödinger equation \[ -Δu+2q u \int_{|x|}^{\infty}\frac{u^{2}(s)}{s}h_u(s)ds +q u\frac{h^{2}_u(|x|)}{|x|^{2}} = g(u), \quad\hbox{in }\mathbb{R}^2, \] where $h_u(s)={\int }_0^s\tau u^2(\tau )d\tau$, under very general assumptions on the nonlinearity $g$. In particular, for every $n\in \mathbb{N}$, we prove the existence of (at least) $n$ distinct solutions, for every $q\in (0,q_n)$, for a suitable $q_n$.

16 pages