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Asymptotic analysis for radial sign-changing solutions of the Brezis-Nirenberg problem in low dimensions

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Contributions to Nonlinear Elliptic Equations and Systems

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 86))

Abstract

We consider the classical Brezis-Nirenberg problem in the unit ball of \(\mathbb{R}^{N}\), N ≥ 3 and analyze the asymptotic behavior of nodal radial solutions in the low dimensions N = 3, 4, 5, 6 as the parameter converges to some limit value which naturally arises from the study of the associated ordinary differential equation.

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Acknowledgements

Research partially supported by MIUR-PRIN project-201274FYK7 005 and GNAMPA-INDAM.

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Authors and Affiliations

  1. Dipartimento di Matematica e Fisica, Università degli Studi di Roma Tre, L.go S. Leonardo Murialdo 1, 00146, Roma, Italy

    Alessandro Iacopetti

  2. Dipartimento di Matematica, Università di Roma “La Sapienza,”, P.le Aldo Moro 5, 00185, Roma, Italy

    Filomena Pacella

Authors
  1. Alessandro Iacopetti
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  2. Filomena Pacella
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Corresponding author

Correspondence to Alessandro Iacopetti .

Editor information

Editors and Affiliations

  1. Universidade de São Paulo, Instituto de Ciências Matemáticas e de Computação, São Carlos, São Paulo, Brazil

    Alexandre Nolasco de Carvalho

  2. Dipartimento di Matematica, Università degli Studi di Milano, Lombardia, Milano, Italy

    Bernhard Ruf

  3. Universidade de São Paulo, Instituto de Ciências Matemáticas e de Computação, São Carlos, São Paulo, Brazil

    Ederson Moreira dos Santos

  4. Département de Mathématique. CP 214, Université Libre de Bruxelles, Brussels, Belgium

    Jean-Pierre Gossez

  5. Universidade de São Paulo, Instituto de Ciências Matemáticas e de Computação, São Carlos, São Paulo, Brazil

    Sergio Henrique Monari Soares

  6. Université Pierre et Marie Curie, Laboratoire Jacques-Louis Lions, Paris, Paris, France

    Thierry Cazenave

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Iacopetti, A., Pacella, F. (2015). Asymptotic analysis for radial sign-changing solutions of the Brezis-Nirenberg problem in low dimensions. In: Nolasco de Carvalho, A., Ruf, B., Moreira dos Santos, E., Gossez, JP., Monari Soares, S., Cazenave, T. (eds) Contributions to Nonlinear Elliptic Equations and Systems. Progress in Nonlinear Differential Equations and Their Applications, vol 86. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-19902-3_20

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