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

2014/07/24 by Patricia L. Cunha, Cunha, Patricia L., Pietro d'Avenia +5
Mathematics · #35J20 #35Q55 #81T10 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35J20 #msc:35Q55 #msc:81T10

paper · pdf · doi:10.48550/arxiv.1407.6629

16 pages

arxiv created 2014/07/24 · arxiv updated 2014/07/25

Abstract

In this paper we give a multiplicity result for the following Chern-Simons-Schrödinger equation -Δu+2q u ∫_|x|^∞\fracu²(s)sh_u(s)ds +q u\frach²_u(|x|)|x|² = g(u), \hboxin ℝ², where h_u(s)=∫₀^s τu²(τ) d τ, under very general assumptions on the nonlinearity g. In particular, for every n∈ \mathbb N, we prove the existence of (at least) n distinct solutions, for every q∈ (0,q_n), for a suitable q_n.

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