Existence of psi-bounded solutions for Sylvester matrix dynamical systems on time scales

Abstract

In this paper, we study the existence criteria for psi -bounded solutions of Sylvester matrix dynamical systems on time scales. The advantage of studying this system is it unifies continuous and discrete systems. First, we prove a necessary and sufficient condition for the existence of at least one psi -bounded solution for Sylvester matrix dynamical systems on time scales, for
every Lebesgue psi- deltaintegrable function F, on time scale T+. Further, we obtain a result relating to asymptotic behavior of  psi-bounded solutions of this system. The results are illustrated with suitable examples.