Multispike solutions for the Brezis-Nirenberg problem in dimension three. (English) Zbl 1394.35145
In this article, the Brezis-Nirenberg problem given by \(\Delta u+\lambda u+u^5=0\) satisfying \(u>0\) in \(\Omega\) with \(u=0\) on the boundary of \(\Omega\) is considered. Here, \(\Omega\) is a smooth and bounded domain in \(\mathbb{R}^3\). The authors establish solutions to this problem which exhibit bubbling behavior at \(n\) different points situated in the domain as \(\lambda\) approaches a special value \(\lambda_0\). The solutions are characterized in terms of the Green function of \(-\Delta-\lambda\).
Reviewer: Andreas Kleefeld (Jülich)
MSC:
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
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