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

Manuel del Pino (), Jean Dolbeault () and Monica Musso ()
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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

A chapter in Nonlinear Differential Equation Models, 2004, pp 57-79 from Springer

Abstract: 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.

Keywords: Brezis-Nirenberg problem; Gelfand problem; supercritical case; bifurcation diagram; singular solutions; Emden-Fowler transform; p-Laplacian; branches of solutions; critical and supercritical problems; dynamical systems; phase plane analysis; bubbles; spikes; multi-peaks; Lyapunov-Schmidt reduction (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7091-0609-9_7

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DOI: 10.1007/978-3-7091-0609-9_7

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