Multipeak solutions for a singularly perturbed Neumann problem

E.N. Dancer and Shusen Yan

Vol. 189 (1999), No. 2, 241–262

DOI: 10.2140/pjm.1999.189.241

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:

(1)

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

Milestones

Received: 12 November 1997

Revised: 29 May 1998

Published: 1 June 1999