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

Del Pino, Manuel; Dolbeault, Jean; Musso, Monica (2004), A Phase Plane Analysis of the “Multi-Bubbling” Phenomenon in Some Slightly Supercritical Equations, Monatshefte für Mathematik, 142, 1-2, p. 57-79. http://dx.doi.org/10.1007/s00605-004-0236-5

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Type
Article accepté pour publication ou publié
Date
2004
Journal name
Monatshefte für Mathematik
Volume
142
Number
1-2
Publisher
Springer
Pages
57-79
Publication identifier
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Author(s)
Del Pino, Manuel
Dolbeault, Jean cc
Musso, Monica
Abstract (EN)
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 nge3 and an equation involving the exponential nonlinearity in dimension nge2. 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.
Subjects / Keywords
Brezis-Nirenberg problem; Gelfand problem; supercritical case; bifurcation diagram; singular solutions; Emden-Fowler transform; p-Laplacian; branches of solutions; critical and super-critical problems; dynamical systems; phase plane analysis; bubbles; spikes; multi-peaks; Lyapunov-Schmidt reduction