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Boundary concentration phenomena for a singularly perturbed elliptic problem
Author(s) -
Malchiodi Andrea,
Montenegro Marcelo
Publication year - 2002
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.10049
Subject(s) - mathematics , bounded function , domain (mathematical analysis) , neumann boundary condition , exponent , boundary (topology) , mathematical analysis , boundary value problem , sequence (biology) , component (thermodynamics) , elliptic curve , mixed boundary condition , free boundary problem , thermodynamics , chemistry , physics , philosophy , linguistics , biochemistry
We exhibit new concentration phenomena for the equation − ε 2 Δ u + u = u p in a smooth bounded domain Ω ⊆ ℝ 2 and with Neumann boundary conditions. The exponent p is greater than or equal to 2 and the parameter ε is converging to 0. For a suitable sequence ε n → 0 we prove the existence of positive solutions u n concentrating at the whole boundary of Ω or at some component. © 2002 Wiley Periodicals, Inc.