Existence of \(\Psi\)-bounded solutions for linear differential systems on time scales

Volume 20, Issue 1, pp 1--13 http://dx.doi.org/10.22436/jmcs.020.01.01
Publication Date: August 11, 2019 Submission Date: April 25, 2019 Revision Date: June 08, 2019 Accteptance Date: June 15, 2019


Kasi Viswanadh V. Kanuri - 3669 Leatherwood, Dr. Frisco, TX 75033, USA. R. Suryanarayana - Department of Mathematics, Vishnu Institute of Technology, Vishnupur, Bhimavaram-534202 Andhra Pradesh, India. K. N. Murty - Department of Applied Mathematics, Andhra University, Waltair, A.P. , India.


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.