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Global bifurcation for a class of nonlinear ODEs

  • Special issue commemorating the Golden Jubilee of the Institute of Mathematics and Statistics of the University of São Paulo
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Abstract

We briefly survey global bifurcation techniques, and illustrate their use by finding multiple positive periodic solutions to a class of second order quasilinear ODEs related to the Yamabe problem. As an application, we give a bifurcation-theoretic proof of a classical nonuniqueness result for conformal metrics with constant scalar curvature, that was independently discovered by Kobayashi and Schoen in the 1980s.

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Authors and Affiliations

  1. Department of Mathematics, City University of New York (Lehman College), 250 Bedford Park Blvd W, Bronx, NY, 10468, USA

    Renato G. Bettiol

  2. Departamento de Matemática, Universidade de São Paulo, Rua do Matão, 1010, São Paulo, SP, 05508-090, Brazil

    Paolo Piccione

Authors
  1. Renato G. Bettiol
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  2. Paolo Piccione
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Correspondence to Paolo Piccione.

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Communicated by Davi Maximo.

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The first-named author was supported by grants from the National Science Foundation (DMS-1904342), PSC-CUNY (Award #62074-00 50), and Fapesp (2019/19891-9). The second named author is partially sponsored by Fapesp (2016/23746-6 and 2019/09045-3) and CNPq, Brazil.

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Bettiol, R.G., Piccione, P. Global bifurcation for a class of nonlinear ODEs. São Paulo J. Math. Sci. 16, 486–507 (2022). https://doi.org/10.1007/s40863-022-00290-3

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  • DOI: https://doi.org/10.1007/s40863-022-00290-3

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