Affiliations: [a] Department of Mathematics, Vishnu Institute of Technology, Bhimavaram 534202, India | [b] Department of CSE, Vignan’s Institute of Information Technology, Visakhapatnam 530049, India | [c] Department of MCA, Vignan’s Institute of Information Technology, Visakhapatnam 530049, India
Correspondence:
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Corresponding author: R. Suryanarayana, Department of Mathematics, Vishnu Institute of Technology, Bhimavaram 534202, India. E-mail: bhavyarsn@gmail.com.
Abstract: In this paper, we establish close relationships between the stability constants on one hand and the global behaviour of fundamental matrices on the other hand to the two-point boundary value problems on time-scale dynamical systems. We introduce the concept of conditioning number k and show that conditioning number is the right criteria in estimating the global error due to small perturbations of two point boundary value problems on time scale dynamical systems. Further, the moderate stability constants imply a dichotomy with moderate k-bound will be developed. Further, the exponential behaviour of solutions of the Green’s matrix will be investigated. We also investigate the conditions under which strong dichotomy exists for two-point boundary value problems when the boundary conditions are separable.
Keywords: Boundary value problems, time-scale dynamical systems
