## Duke Mathematical Journal

### Multidimensional boundary layers for a singularly perturbed Neumann problem

#### 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

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

#### 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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