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Singular Solutions of the Scalar Field Equation with a Critical Exponent

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Geometric Properties for Parabolic and Elliptic PDE's (GPPEPDEs 2015)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 176))

Abstract

We consider radially symmetric singular solutions of the scalar field equation with the Sobolev critical exponent. It is shown that there exists a unique special singular solution, and other infinitely many singular solutions are oscillatory around the special singular solution.

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Acknowledgments

The first author was supported in part by MOST of Taiwan (No. MOST 104-2115-M-008-010-MY3). The second author was supported in part by JSPS KAKHENHI Grant-in-Aid for Scientific Research (A) (No. 24244012).

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Authors and Affiliations

  1. Department of Mathematics, National Central University, 32001, Chung-Li, Taiwan, China

    Jann-Long Chern

  2. Department of Mathematics, Tokyo Institute of Technology, Meguro-ku, Tokyo, 152-8551, Japan

    Eiji Yanagida

Authors
  1. Jann-Long Chern
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  2. Eiji Yanagida
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Corresponding author

Correspondence to Eiji Yanagida .

Editor information

Editors and Affiliations

  1. Dipartimento di Matematica, Politecnico di Milano, Milano, Milano, Italy

    Filippo Gazzola

  2. Mathematical Institute, Tohoku University, Sendai, Japan

    Kazuhiro Ishige

  3. Dip. di Matematica e Applicazioni, Università degli Studi di Napoli Federico II, Monte S. Angelo, Napoli, Italy

    Carlo Nitsch

  4. Dipartimento di Matematica Ulisse Dini, Università degli Studi di Firenze, Firenze, Firenze, Italy

    Paolo Salani

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Chern, JL., Yanagida, E. (2016). Singular Solutions of the Scalar Field Equation with a Critical Exponent. In: Gazzola, F., Ishige, K., Nitsch, C., Salani, P. (eds) Geometric Properties for Parabolic and Elliptic PDE's. GPPEPDEs 2015. Springer Proceedings in Mathematics & Statistics, vol 176. Springer, Cham. https://doi.org/10.1007/978-3-319-41538-3_16

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