Abstract
In this paper we give a multiplicity result for the following Chern–Simons–Schrödinger equation
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 .
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P. d’Avenia and A. Pomponio are supported by GNAMPA project “Aspetti differenziali e geometrici nello studio di problemi ellittici quasilineari”. G. Siciliano is supported by Fapesp (SP) and CNPq, Brazil.
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Cunha, P.L., d’Avenia, P., Pomponio, A. et al. A multiplicity result for Chern–Simons–Schrödinger equation with a general nonlinearity. Nonlinear Differ. Equ. Appl. 22, 1831–1850 (2015). https://doi.org/10.1007/s00030-015-0346-x
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DOI: https://doi.org/10.1007/s00030-015-0346-x