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15 July 2004 Multidimensional boundary layers for a singularly perturbed Neumann problem
Andrea Malchiodi, Marcelo Montenegro
Duke Math. J. 124(1): 105-143 (15 July 2004). DOI: 10.1215/S0012-7094-04-12414-5

Abstract

We continue the study of [34], proving concentration phenomena for the equation − ε2 Δu + u = up in a smooth bounded domain Ω ⊆ $\mathbb{R}^n$ and with Neumann boundary conditions. The exponent p is greater than or equal to 1, and the parameter ε is converging to zero. For a suitable sequence εj → 0, we prove the existence of positive solutions uj concentrating at the whole boundary of Ω or at some of its components.

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Andrea Malchiodi. Marcelo Montenegro. "Multidimensional boundary layers for a singularly perturbed Neumann problem." Duke Math. J. 124 (1) 105 - 143, 15 July 2004. https://doi.org/10.1215/S0012-7094-04-12414-5

Information

Published: 15 July 2004
First available in Project Euclid: 30 July 2004

zbMATH: 1065.35037
MathSciNet: MR2072213
Digital Object Identifier: 10.1215/S0012-7094-04-12414-5

Subjects:
Primary: 35B25, 35B34, 35J20, 35J60

Rights: Copyright © 2004 Duke University Press

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Vol.124 • No. 1 • 15 July 2004
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