Existence of \(\Psi\)-bounded solutions for linear differential systems on time scales
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Authors
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.
Abstract
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.
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ISRP Style
Kasi Viswanadh V. Kanuri, R. Suryanarayana, K. N. Murty, Existence of \(\Psi\)-bounded solutions for linear differential systems on time scales, Journal of Mathematics and Computer Science, 20 (2020), no. 1, 1--13
AMA Style
Kanuri Kasi Viswanadh V., Suryanarayana R., Murty K. N., Existence of \(\Psi\)-bounded solutions for linear differential systems on time scales. J Math Comput SCI-JM. (2020); 20(1):1--13
Chicago/Turabian Style
Kanuri, Kasi Viswanadh V., Suryanarayana, R., Murty, K. N.. "Existence of \(\Psi\)-bounded solutions for linear differential systems on time scales." Journal of Mathematics and Computer Science, 20, no. 1 (2020): 1--13
Keywords
- \(\Psi\)-bounded
- \(\Psi\)-integrable
- Lebesgue \(\Psi\)-delta integrable
MSC
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