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

  • Patricia L. Cunha
  • Pietro d’Avenia
  • Alessio Pomponio
  • Gaetano Siciliano


In this paper we give a multiplicity result for the following Chern–Simons–Schrödinger equation
$$-\Delta u + 2q u \int_{|x|}^{\infty}\frac{u^{2}(s)}{s}h_u(s)ds + q u \frac{h^{2}_u(|x|)}{|x|^{2}} = g(u), \quad {\rm in} \mathbb{R}^2,$$
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 .


Chern–Simons gauge field Schrödinger equation Variational methods Radial solutions General nonlinearities 

Mathematics Subject Classification

35J20 35Q55 81T10 


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Copyright information

© Springer Basel 2015

Authors and Affiliations

  • Patricia L. Cunha
    • 1
  • Pietro d’Avenia
    • 2
  • Alessio Pomponio
    • 2
  • Gaetano Siciliano
    • 3
  1. 1.Departamento de Informática e Métodos QuantitativosFundação Getulio VargasSão PauloBrazil
  2. 2.Dipartimento di Meccanica, Matematica e ManagementPolitecnico di BariBariItaly
  3. 3.Departamento de MatemáticaUniversidade de São PauloSão PauloBrazil

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