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On Singular Liouville Systems

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Analysis and Topology in Nonlinear Differential Equations

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 85))

Abstract

We discuss a class of planar systems of Liouville type in presence of singular sources. When the coupling matrix admits positive entries, we provide necessary and sufficient conditions for the existence of radial solutions and corresponding uniqueness. For this purpose we point out a log HLS inequality in system’s form that involves weights and holds in the radial setting.

Mathematics Subject Classification (2010). 35J47, 35J61, 34A34, 47J20.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Ben Gurion University of the Negev, 653, Be’er Sheva, 84105, Israel

    A. Poliakovsky

  2. Dipartimento di Matematica, Università degli Studi di Roma “Tor Vergata”, via della Ricerca Scientifica, I-00133, Rome, Italy

    G. Tarantello

Authors
  1. A. Poliakovsky
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  2. G. Tarantello
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Correspondence to A. Poliakovsky .

Editor information

Editors and Affiliations

  1. IMECC-UNICAMP, Cidade Universitaria Instituto de Matematica, Estatistica e C, Campinas, São Paulo, Brazil

    Djairo G de Figueiredo

  2. Departamento de Matemática - CCEN, Universidade Federal da Paraíba, João Pessoa, Paraíba, Brazil

    João Marcos do Ó

  3. Departamento de Matemática, Pontifícia Universidade Católica do Rio, Rio de Janeiro, Rio de Janeiro, Brazil

    Carlos Tomei

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Poliakovsky, A., Tarantello, G. (2014). On Singular Liouville Systems. In: de Figueiredo, D., do Ó, J., Tomei, C. (eds) Analysis and Topology in Nonlinear Differential Equations. Progress in Nonlinear Differential Equations and Their Applications, vol 85. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-04214-5_22

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