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