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Title: Global asymptotic stability for semilinear equations via Thompson's metric
Authors: Herzog, G.
Kunstmann, P.C.
Keywords: Ordered Banach spaces;Thompson metric;Global stability;Semilinear equations;Espacios de Banach ordenados;Métrica de Thompson;Estabilidad global;Ecuaciones semilineales
Issue Date: 2014
Publisher: Extracta Mathematicae
Abstract: In ordered Banach spaces we prove the global asymptotic stability of the unique strictly positive equilibrium of the semilinear equation u′ = Au + ꭍ(u), if A is the generator of a positive and exponentially stable C₀-semigroup and ꭍ is a contraction with respect to Thompson's metric. The given estimates show that convergence holds with a uniform exponential rate.
Appears in Collections:Extracta Mathematicae Vol. 29, nº 1-2 (2014)

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