“ Bubble-tower ” Radial Solutions in the Slightly Supercritical Brezis-nirenberg Problem

@inproceedings{Pino2007B,
title={“ Bubble-tower ” Radial Solutions in the Slightly Supercritical Brezis-nirenberg Problem},
author={Manuel M S{\'a}nchez Del Pino and Jean Dolbeault and Monica Musso},
year={2007}
}

In this paper, we consider the Brezis-Nirenberg problem in dimension N ≥ 4, in the supercritical case. We prove that if the exponent gets close to N+2 N−2 and if, simultaneously, the bifurcation parameter tends to zero at the appropriate rate, then there are radial solutions which behave like a superposition of bubbles, namely solutions of the form

Positive solutions of elliptic equations involving supercritical growth

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Asymptotics for elliptic equations involving critical growth

H. Brezis, L. A. Peletier

Partial differential equations and the calculus of variations, Vol. I, 149–192, Progr. Nonlinear Differential Equations Appl., 1, Birkhauser Boston • 1989