Sign-changing tower of bubbles for the Brezis-Nirenberg problem
Analysis of PDEs
2014-12-04 v3
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.
Keywords
Cite
@article{arxiv.1402.1451,
title = {Sign-changing tower of bubbles for the Brezis-Nirenberg problem},
author = {Alessandro Iacopetti and Giusi Vaira},
journal= {arXiv preprint arXiv:1402.1451},
year = {2014}
}