Global Asymptotic Stability for Semilinear Equations via Thompson’s Metric

• G. Herzog ^[1] ; P.C. Kunstmann ^[1]
  1. [1] Karlsruher Institut für Technologie (KIT). Germany
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 29, Nº 1-2, 2014, págs. 141-157
• Idioma: inglés
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• Resumen

  • In ordered Banach spaces we prove the global asymptotic stability of the unique strictly positive equilibrium of the semilinear equation u ′ = Au + f(u), if A is the generator of a positive and exponentially stable C0-semigroup and f is a contraction with respect to Thompson’s metric. The given estimates show that convergence holds with a uniform exponential rate.