Published in
Nonlinear Differential Equation Models, p. 57-79
DOI: 10.1007/978-3-7091-0609-9_7
Springer Verlag, Monatshefte für Mathematik, 1-2(142), p. 57-79
DOI: 10.1007/s00605-004-0236-5
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A phase plane analysis of the "multi-bubbling" phenomenon in some slightly supercritical equations
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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 n3 and an equation involving the exponential nonlinearity in dimension n2. 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.