Nonlinear elliptic problems on singularly perturbed domains
Published online by Cambridge University Press: 12 July 2007
Abstract
We consider how the shape of a domain affects the number of positive solutions of a nonlinear elliptic problem. In fact, we show that if a bounded domain Ω is sufficiently close to a union of disjoint bounded domains Ω1,…, Ωm, the number of positive solutions of a nonlinear elliptic problem on Ω is at least 2m −1.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 131 , Issue 5 , October 2001 , pp. 1023 - 1037
- Copyright
- Copyright © Royal Society of Edinburgh 2001
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