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. 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

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