Resumen de Global Asymptotic Stability for Semilinear Equations via Thompson’s Metric

Gerd Herzog, P.C. Kunstmann

• 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.