General Uniqueness results and Variation Speed for Blow-up Solutions of Elliptic Equations

Abstract

Let Ω ⊂ ℝN (N ≥ 2) be a smooth bounded domain. We are interested in the uniqueness and asymptotic behavior of the blow-up solutions to the equation -Δu=au-b(x)f(u)in Ω (1) where f∈C[0, ∞ ) is locally Lipschitz, a ∈ ℝ is a parameter and b ∈C⁰... (0 < μ < 1) is positive in Ω and non-negative on ∂Ω.