A multiplicity result for Chern-Simons-Schr\"odinger equation with a general nonlinearity

In this paper we give a multiplicity result for the following Chern-Simons-Schr"odinger equation $$-\mathrm{\Delta }u+2qu{\int }_{\mathrm{\mid }x\mathrm{\mid }}^{\mathrm{\infty }}\frac{u^2(s)}{s}{h}_u(s)ds+qu\frac{h_u^2(\mathrm{\mid }x\mathrm{\mid })}{\mathrm{\mid }x{\mathrm{\mid }}^2}=g(u),\text{in }{\mathbb{R}}^2,$$ where $\displaystyle h_u(s)=\int_0^s \tau u^2(\tau) \ d \tau$,underverygeneralassumptionsonthenonlinearity$g$\mathrm{.}Inparticular,forevery$n\in \mathbb N$, we prove the existence of (at least) $n$ distinct solutions, for every $q\in (0,q_n)$, for a suitable $q_n$.