"Bubble-tower" radial solutions in the slightly supercritical Brezis-Nirenberg problem

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Abstract

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 A figure is presented. where Mj → + ∞ and Mj = o(Mj+1) for all j. These solutions lie close to turning points "to the right" of the associated bifurcation diagram. © 2003 Elsevier Inc. All rights reserved.

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Del Pino, M., Dolbeault, J., & Musso, M. (2003). “Bubble-tower” radial solutions in the slightly supercritical Brezis-Nirenberg problem. Journal of Differential Equations, 193(2), 280–306. https://doi.org/10.1016/S0022-0396(03)00151-7

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