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

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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

34D05
34C11

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