Duke Mathematical Journal
- Duke Math. J.
- Volume 124, Number 1 (2004), 105-143.
Multidimensional boundary layers for a singularly perturbed Neumann problem
Andrea Malchiodi and Marcelo Montenegro
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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.
Article information
Source
Duke Math. J., Volume 124, Number 1 (2004), 105-143.
Dates
First available in Project Euclid: 30 July 2004
Permanent link to this document
https://projecteuclid.org/euclid.dmj/1091217476
Digital Object Identifier
doi:10.1215/S0012-7094-04-12414-5
Mathematical Reviews number (MathSciNet)
MR2072213
Zentralblatt MATH identifier
1065.35037
Subjects
Primary: 35B25: Singular perturbations 35B34: Resonances 35J20: Variational methods for second-order elliptic equations 35J60: Nonlinear elliptic equations
Citation
Malchiodi, Andrea; Montenegro, Marcelo. Multidimensional boundary layers for a singularly perturbed Neumann problem. Duke Math. J. 124 (2004), no. 1, 105--143. doi:10.1215/S0012-7094-04-12414-5. https://projecteuclid.org/euclid.dmj/1091217476
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