On the Dichotomy of Non-Autonomous Systems Over Finite Dimensional Spaces

Authors

Akbar Zada, Department of Mathematics, University of Peshawar, Peshawar, PakistanFollow
Sadia Arshad, Department of Mathematics, COMSATS Institute of Information Technology, Lahore, PakistanFollow
Gul Rahmat, Department of Mathematics, Islamia college University Peshawar, Peshawar, PakistanFollow
Aftab Khan, Department of Mathematics, Shaheed Benazir Bhutto University, Sheringal, Dir, PakistanFollow

Author Country (or Countries)

Pakistan

Abstract

In this article we study the dichotomy of the q periodic system ˙X (t) = A(t)X(t) in terms of the boundedness of the solutions of the following Cauchy problems ˙X (t) = A(t)X(t)+eimtPb, t ≥ 0 X(0) = 0, and ˙X (t) = −X(t)A(t)+eimt (I−P)b, t ≥ 0 X(0) = 0, where A(t) is a square size matrix of order m, m is any real number, b is a non zero vector in Cm and P is an orthogonal projection.

Recommended Citation

Zada, Akbar; Arshad, Sadia; Rahmat, Gul; and Khan, Aftab (2015) "On the Dichotomy of Non-Autonomous Systems Over Finite Dimensional Spaces," Applied Mathematics & Information Sciences: Vol. 09: Iss. 4, Article 33.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss4/33