Boundary Concentration in Radial Solutions to a System of Semilinear Elliptic Equations | Zendy

D'Aprile Teresa | Zendy; Wei Juncheng | Zendy

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Boundary Concentration in Radial Solutions to a System of Semilinear Elliptic Equations

Author(s) -

D'Aprile Teresa,

Wei Juncheng

Publication year - 2006

Publication title -

journal of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.441

H-Index - 62

eISSN - 1469-7750

pISSN - 0024-6107

DOI - 10.1112/s0024610706023027

Subject(s) - dirichlet boundary condition , mathematics , mathematical analysis , unit sphere , boundary (topology) , boundary value problem , dirichlet distribution , ball (mathematics) , reduction (mathematics) , lyapunov function , physics , geometry , nonlinear system , quantum mechanics

We study concentration phenomena for the systemε 2 Δ υ − υ − δ φ υ + γ υ p = 0 , Δ φ + δ υ 2 = 0in the unit ball B 1 of ℝ 3 with Dirichlet boundary conditions. Here ɛ, δ, γ > 0 and p > 1. We prove the existence of positive radial solutions (υɛ, φɛ) such that υɛ concentrates at a distance (ɛ/2)|log ɛ| away from the boundary ∂ B 1 as the parameter ɛ tends to 0. The approach is based on a combination of Lyapunov–Schmidt reduction procedure together with a variational method.

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