%0 Journal Article %T Existence of \(\Psi\)-bounded solutions for linear differential systems on time scales %A Kanuri, Kasi Viswanadh V. %A Suryanarayana, R. %A Murty, K. N. %J Journal of Mathematics and Computer Science %D 2020 %V 20 %N 1 %@ ISSN 2008-949X %F Kanuri2020 %X In this paper, we define \(\Psi \)-boundedness on time scales and we present necessary and sufficient conditions for the existence of at least one \(\Psi\)-bounded solution for the linear non-homogeneous matrix system \(x^{\Delta}=A(t)x + f(t)\), where f(t) is a \(\Psi\)-bounded matrix valued function on \({T}\) assuming that \(f\) is a Lebesgue \(\Psi\)-delta integrable function on time scale \({T}\). Finally we give a result in connection with the asymptotic behavior of the \(\Psi\)-bounded solutions of this system. %9 journal article %R 10.22436/jmcs.020.01.01 %U http://dx.doi.org/10.22436/jmcs.020.01.01 %P 1--13