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arXiv · 1402.1451

Sign-changing tower of bubbles for the Brezis-Nirenberg problem

Alessandro Iacopetti·Giusi Vaira
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Abstract

In this paper, we prove that the Brezis-Nirenberg problem -\Delta u = |u|^{p-1}u+\epsilon u in \Omega; u=0 on \partial \Omega where \Omega is a symmetric bounded smooth domain in R^N, N\geq 7 and p = (N+2)/(N-2), has a solution with the shape of a tower of two bubbles with alternate signs, centered at the center of symmetry of the domain, for all \epsilon > 0 sufficiently small.

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Alessandro Iacopetti, Giusi Vaira. 2014-02-06. Sign-changing tower of bubbles for the Brezis-Nirenberg problem. https://arxiv.org/abs/1402.1451

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