Abstract
In this paper we consider the existence and uniqueness of global solutions to linear dynamical equations for a Banach space on time scales from a new point of view. We characterize those linear dynamical equations for a Banach space whose existence and uniqueness of global solutions do not depend on concrete time scales.MSC:34G10, 34K30, 39A13.
Highlights
The calculus of time scales was introduced by Hilger in his PhD dissertation [ ] in order to unify continuous and discrete analysis
In [, ], Hilger obtained the existence and uniqueness conditions for the global solutions to nonlinear and linear dynamical equations, while the conditions are closely dependent on the concrete time scales
It is natural to ask whether or not there exists a class of equations whose existence and uniqueness of global solutions do not depend on the concrete time scales
Summary
The calculus of time scales was introduced by Hilger in his PhD dissertation [ ] in order to unify continuous and discrete analysis. For linear dynamical equations in finite-dimensional spaces on time scales, a lot of results have been obtained (see [ – , – ]). While for dynamical equations in Banach spaces on time scales, only a few results have been obtained (see [ , , ]).
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