Vol. 189, No. 2, 1999

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ISSN: 0030-8730
Multipeak solutions for a singularly perturbed Neumann problem

E.N. Dancer and Shusen Yan

Vol. 189 (1999), No. 2, 241–262
Abstract

The aim of this paper is to prove the existence of k-peak solutions (solutions with more than one local maximum point) for the following singularly perturbed problem without imposing any extra condition on the boundary Ω:

(
|{ − 𝜀2Δu + u = up− 1, in Ω
u > 0,            in Ω
|( ∂u
∂n = 0,           on ∂ Ω
(1)

where 𝜀 is a small positive number, Ω is a bounded C3-domain in RN, n is the unit outward normal of Ω at y,2 < p < -2N-
N −2 if N 3 and 2 < p < +if N = 2.

Milestones
Received: 12 November 1997
Revised: 29 May 1998
Published: 1 June 1999
Authors
E.N. Dancer
Shusen Yan
School of Mathematics and Statistics
University of Sydney
NSW 2006
Australia