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Nonlinear elliptic problems on singularly perturbed domains

Published online by Cambridge University Press:  12 July 2007

Jaeyoung Byeon
Jaeyoung Byeon
Affiliation:
Department of Mathematics, POSTECH, San 31 Hyoja-dong, Nam-gu, Pohang, Kyungbuk 790–784, Republic of Korea and Korea Institute for Advanced Study (jbyeon@postech.ac.kr)
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Abstract

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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