Title

High-energy and multi-peaked solutions for a nonlinear Neumann problem with critical exponents

Document Type

Article

Journal/Book Title/Conference

Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Volume

125

Issue

5

Publisher

Cambridge University Press

Publication Date

1995

Grant Number

DMS-9201283

Funder

NSF

First Page

1003

Last Page

1029

DOI

http://dx.doi.org/10.1017/S0308210500022617

Abstract

We establish the existence of positive solutions with two peaks being located on the boundary of the domain for the problem -Δu + λu = up in antipodal invariant domains including ball domains with Neumann boundary conditions. Here p is the critical Sobolev exponent (N + 2)/(N - 2). The shape of the solutions and the location of the peaks are also studied.