The Effect of the Domain Topology on the Number of Minimal Nodal Solutions of an Elliptic Equation at Critical Growth in a Symmetric Domain

Authors

Alfonso Castro, Harvey Mudd CollegeFollow
Mónica Clapp, Universidad Nacional Autonoma de Mexico

Document Type

Article - postprint

Department

Mathematics (HMC)

Publication Date

1-2003

Abstract

We consider the Dirichlet problem Δu + λu + |u|^2*−2u = 0 in Ω, u = 0 on ∂Ω where Ω is a bounded smooth domain in R^N, N≥4, and 2* = 2N/(N−2) is the critical Sobolev exponent. We show that if Ω is invariant under an orthogonal involution then, for λ>0 sufficiently small, there is an effect of the equivariant topology of Ω on the number of solutions which change sign exactly once.

Comments

Author's post-print manuscript available for download.

For the publisher's PDF, please visit http://dx.doi.org/10.1088/0951-7715/16/2/313.

Rights Information

© 2003 IOP Publishing

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DOI

10.1088/0951-7715/16/2/313

Recommended Citation

Castro, Alfonso and Monica Clapp. “The effect of the domain topology on the number of minimal nodal solutions of an elliptic equation at critical growth in a symmetric domain”, Nonlinearity 16(2003), 579-590.