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A Multiplicity Result for Singularly Perturbed Problems in Topologically Nontrivial Domains

Giovanna Cerami and Riccardo Molle

Abstract

The problem − ε2Δu + aε(x)u = up−1 with zero Dirichlet boundary condition is considered in a nontrivial bounded domain Ω ⊂ ℝN. Under the assumption that aε(x) ≥ a0 > 0 concentrates at a point of Ω as ε → 0 and has a suitable behaviour at infinity and, moreover, that p > 2 and if N ≥ 3, the existence of at least (cat Ω̅) + 2 distinct positive solutions is proved.

Received: 2004-5-20
Published Online: 2016-3-10
Published in Print: 2004-11-1

© 2016 by Advanced Nonlinear Studies, Inc.