Boundary concentration phenomena for a singularly perturbed elliptic problem | Zendy

Malchiodi Andrea | Zendy; Montenegro Marcelo | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Premium

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.

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here

Accelerating Research