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A Lane–Emden system with singular data

Published online by Cambridge University Press:  15 November 2011

Marius Ghergu
Affiliation:
School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland (marius.ghergu@ucd.ie)

Abstract

We study the elliptic system −Δu = δ(x)−avp in Ω, −Δv = δ(x)−buq in Ω, subject to homogeneous Dirichlet boundary conditions. Here, Ω ⊂ ℝN, N ≥ 1, is a smooth and bounded domain, δ(x) = dist(x, ∂Ω), a, b ≥ 0 and p, q ∈ ℝ satisfy pq > −1. The existence, non-existence and uniqueness of solutions are investigated in terms of a, b, p and q.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2011

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