caa a22 4500 606193898 CHVBK 20210128100911.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s00030-015-0346-x doi (NATIONALLICENCE)springer-10.1007/s00030-015-0346-x A multiplicity result for Chern-Simons-Schrödinger equation with a general nonlinearity [Elektronische Daten] [Patricia Cunha, Pietro d'Avenia, Alessio Pomponio, Gaetano Siciliano] In this paper we give a multiplicity result for the following Chern-Simons-Schrödinger equation $$-\Delta u + 2q u \int_{|x|}^{\infty}\frac{u^{2}(s)}{s}h_u(s)ds + q u \frac{h^{2}_u(|x|)}{|x|^{2}} = g(u), \quad {\rm in} \mathbb{R}^2,$$ - Δ u + 2 q u ∫ | x | ∞ u 2 ( s ) s h u ( s ) d s + q u h u 2 ( | x | ) | x | 2 = g ( u ) , in R 2 , where $${h_u(s) = \int_0^s \tau u^2(\tau)\, d\tau}$$ h u ( s ) = ∫ 0 s τ u 2 ( τ ) d τ , under very general assumptions on the nonlinearity g. In particular, for every $${n \in \mathbb{N}}$$ n ∈ N , we prove the existence of (at least) n distinct solutions, for every $${q \in (0, q_{n})}$$ q ∈ ( 0 , q n ) , for a suitable q n . Springer Basel, 2015 Chern-Simons gauge field nationallicence Schrödinger equation nationallicence Variational methods nationallicence Radial solutions nationallicence General nonlinearities nationallicence Cunha Patricia Departamento de Informática e Métodos Quantitativos, Fundação Getulio Vargas, Av. Nove de Julho, 2029 - Bela Vista, 01313-902, São Paulo, SP, Brazil aut d'Avenia Pietro Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, Via E. Orabona 4, 70125, Bari, Italy aut Pomponio Alessio Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, Via E. Orabona 4, 70125, Bari, Italy aut Siciliano Gaetano Departamento de Matemática, Universidade de São Paulo, Rua do Matão, 1010 - Cidade Universitaria, 05508-090, São Paulo, SP, Brazil aut Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/6(2015-12-01), 1831-1850 1021-9722 22:6<1831 2015 22 30 https://doi.org/10.1007/s00030-015-0346-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00030-015-0346-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Cunha Patricia Departamento de Informática e Métodos Quantitativos, Fundação Getulio Vargas, Av. Nove de Julho, 2029 - Bela Vista, 01313-902, São Paulo, SP, Brazil aut NATIONALLICENCE 700 1- d'Avenia Pietro Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, Via E. Orabona 4, 70125, Bari, Italy aut NATIONALLICENCE 700 1- Pomponio Alessio Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, Via E. Orabona 4, 70125, Bari, Italy aut NATIONALLICENCE 700 1- Siciliano Gaetano Departamento de Matemática, Universidade de São Paulo, Rua do Matão, 1010 - Cidade Universitaria, 05508-090, São Paulo, SP, Brazil aut NATIONALLICENCE 773 0- Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/6(2015-12-01), 1831-1850 1021-9722 22:6<1831 2015 22 30