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Multiple boundary peak solutions for some singularly perturbed Neumann problems

✍ Scribed by Changfeng Gui; Juncheng Wei; Matthias Winter


Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
210 KB
Volume
17
Category
Article
ISSN
0294-1449

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✦ Synopsis


We first use the Liapunov-Schmidt method to reduce the problem to finite dimensions. Then we use a maximizing procedure to obtain multiple boundary spikes.


πŸ“œ SIMILAR VOLUMES


Multiple positive solutions for singular
✍ Giovanna Cerami; Riccardo Molle πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 149 KB

The equation -Ξ΅ 2 u + a Ξ΅ (x)u = u p-1 with boundary Dirichlet zero data is considered in an exterior domain = R N \ Ο‰ (Ο‰ bounded and N 2). Under the assumption that a Ξ΅ a 0 > 0 concentrates round a point of as Ξ΅ β†’ 0, that p > 2 and p < 2N/(N -2) when N 3, the existence of at least three positive di