Nonlinear elliptic problems on singularly perturbed domains
Jaeyoung Byeon · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 2001
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.