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

Abstract

In this paper we give a multiplicity result for the following Chern-Simons-Schrodinger equation -Delta u + 2qu integral(infinity)(vertical bar x vertical bar) u(2) (s)/s h(u)(s) ds + qu h(u)(2)(vertical bar x vertical bar)/vertical bar x vertical bar(2) = g(u), in R-2, where h(u)(s) = integral(s)(0) tu(2)(tau) d tau, under very general assumptions on the nonlinearity g. In particular, for every n is an element of N, we prove the existence of (at least) n distinct solutions, for every q is an element of(0, q(n)), for a suitable q(n).