Uniqueness and layer analysis for boundary blow-up solutions

Abstract We prove uniqueness for boundary blow-up solutions of the problem: Δ u=λf(u) in Ω, u| ∂Ω =∞, with large λ. Previous uniqueness results require a monotonicity assumption for f(u)/u in the entire range of the boundary blow-up solutions. By obtaining good boundary layer estimates for large λ, we obtain uniqueness under much weaker assumptions on f(u). Our estimates for the layers of the boundary blow-up solutions have independent interest, and may have other applications.

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