Vol. 200, No. 1, 2001

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Existence and nonexistence of interior-peaked solution for a nonlinear Neumann problem

Daomin Cao, E.S. Noussair and Shusen Yan

Vol. 200 (2001), No. 1, 19–42
Abstract

We show that the critical problem

{
− Δu + λu = u2∗−1 + auq−1, u > 0 in Ω,
∂u = 0  on ∂Ω, 2 < q < 2∗ = 2N∕(N − 2),
∂ν

has no positive solutions concentrating, as λ →∞, at interior points of Ω if a = 0, but for a class of symmetric domains Ω, the problem with a > 0 has solutions concentrating at interior points of Ω.

Milestones
Received: 27 September 1999
Revised: 28 February 2000
Published: 1 September 2001
Authors
Daomin Cao
Institute of Applied Mathematics
Academy of Mathematics and System Sciences
Chinese Academy of Sciences
Beijing 100080
P.R.China
E.S. Noussair
School of Mathematics
University of New South Wales
Sydney NSW 2052
Australia
Shusen Yan
School of Mathematics and Statistics
University of Sydney
NSW 2006
Australia