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.
Citation
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
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