David Cheban
Asymptotic Stability of Generalized Homogeneous Nonautonomous Dynamical Systems
Dynamic Systems and Applications 33 (2024)   119-158

https://doi.org/10.46719/dsa2024.33.06

ABSTRACT.
The goal of the paper is to study the relationship between asymptotic stability and exponential stability of the solutions of generalized infinite-dimensional homogeneous nonautonomous dynamical systems. This problem is studied and solved within the framework of general non-autonomous (cocycle) dynamical system. The application of our general results for functional differential and semi-linear parabolic equations is given.

AMS (MOS)Subject Classification. 34K04, 34K20, 35A16, 35A24, 35B06, 35B35, 35B40, 37B25, 37B55, 37C75.

Key Words and Phrases. Uniform Asymptotic Stability; Global Attractor, Homogeneous Dynamical System.