Dichotomy of Poincare map and boundedness of solutions of certain non-autonomous periodic cauchy problems
Akbar Zada, Sadia Arshad, Gul Rahmat, Aftab Khan
TL;DR
This paper investigates the relationship between the dichotomy of Poincaré maps and the boundedness of solutions in certain non-autonomous periodic Cauchy problems, providing theoretical insights into their connection.
Contribution
It establishes a new relation linking the dichotomy of Poincaré maps with the boundedness of solutions in specific periodic Cauchy problems.
Findings
Dichotomy of Poincaré map implies boundedness of solutions
Bounded solutions correspond to certain properties of the Poincaré map
Provides a theoretical framework connecting stability and solution boundedness
Abstract
In this paper we study the dichotomy of Poincarce map. We give a relation between the dichotomy of the Poincarce map and boundedness of solutions of certain periodic Cauchy problems
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Taxonomy
TopicsNonlinear Differential Equations Analysis · Advanced Differential Equations and Dynamical Systems · Stability and Controllability of Differential Equations