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Multiple sign-changing solutions for a semilinear Neumann problem and the topology of the configuration space of the domain boundary

✍ Scribed by Naoki Shioji


Publisher
Springer
Year
2009
Tongue
English
Weight
482 KB
Volume
38
Category
Article
ISSN
0944-2669

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We consider the problem: \(-\Delta u+\lambda u=u^{(n+2) /(n-2)}, u>0\) in \(\Omega, \partial u / \hat{\partial} v=0\) on \(\partial \Omega\), where \(\Omega\) is a bounded smooth domain in \(\mathbb{R}^{n}(n \geqslant 3)\). We show that, for \(\lambda\) large, least-energy solutions of the above pro