Derivatives of Solutions of $n$th Order Dynamic Equations on Time Scales
DOI:
https://doi.org/10.5644/SJM.19.02.05Keywords:
continuous dependence, variational equation, delta derivative, time scaleAbstract
(Delta) derivatives of the solutions to an $n$th order parameter dependent dynamic equation on an arbitrary time scale are shown to exist with respect to the boundary data. This result is achieved by standard uniqueness and continuity assumptions. Moreover, these (delta) derivatives are shown to solve an associated homogeneous and nonhomogeneous dynamic equation on the same time scale.
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