2009/05/29 by António J. G. Bento, Bento, António J. G., César Silva +1
Computer Science · Engineering · Mathematics · #34D09 #37D10 #37D25 #Advanced Mathematical Modeling in Engineering #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Biology Tumor Growth #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.0905.4935
openalex publication_date 2009/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Assuming the existence of a general nonuniform dichotomy for the evolution operator of a non-autonomous ordinary linear differential equation in a Banach space, we establish the existence of invariant stable manifolds for the semiflow generated by sufficiently small nonlinear perturbations of the linear equation. The family of dichotomies considered satisfies a general growth rate given by some increasing differentiable function, allows situations for which the classical Lyapunov exponents are zero, and contains the nonuniform exponential dichotomies as a very particular case. In addition we also give explicit examples of linear equations that admit all the possible considered dichotomies.