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A Phase Plane Analysis of the “Multi-Bubbling” Phenomenon in Some Slightly Supercritical Equations

In: Nonlinear Differential Equation Models

Author

Listed:
  • Manuel del Pino

    (Universidad de Chile, Departamento de Ingeniería Matemática and CMM)

  • Jean Dolbeault

    (Universite Paris IX-Dauphine, Ceremade (UMR CNRS no. 7534))

  • Monica Musso

    (Politecnico di Torino, Dipartimento di Matematica)

Abstract

The purpose of this paper is to present some recent results in two slightly super-critical problems known as the Brezis-Nirenberg problem in dimension n⩾3 and an equation involving the exponential nonlinearity in dimension n⩾2. For that purpose, we perform a phase plane analysis which emphasizes the common heuristic properties of the two problems, although more precise estimates can be obtained in some cases by variational methods.

Suggested Citation

  • Manuel del Pino & Jean Dolbeault & Monica Musso, 2004. "A Phase Plane Analysis of the “Multi-Bubbling” Phenomenon in Some Slightly Supercritical Equations," Springer Books, in: Ansgar Jüngel & Raul Manasevich & Peter A. Markowich & Henrik Shahgholian (ed.), Nonlinear Differential Equation Models, pages 57-79, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7091-0609-9_7
    DOI: 10.1007/978-3-7091-0609-9_7
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