Differentiation of solutions of dynamic equations on time scales with respect to parameters

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Authors	ŠIMON HILSCHER Roman KRATZ Werner ZEIDAN Vera Michel
Year of publication	2009
Type	Article in Periodical
Magazine / Source	Advances in Dynamical Systems and Applications
MU Faculty or unit	Faculty of Science
Citation	ŠIMON HILSCHER, Roman, Werner KRATZ and Vera Michel ZEIDAN. Differentiation of solutions of dynamic equations on time scales with respect to parameters. Advances in Dynamical Systems and Applications. Delhi (Indie): Research India Publications, 2009, vol. 4, No 1, p. 35-54. ISSN 0973-5321.
Field	General mathematics
Keywords	Time scale; Embedding theorem; Differentiation with respect to parameters; Entire function; Complex domain
Description	In this paper we prove the differentiability properties of solutions of nonlinear dynamic equations on time scales with respect to parameters. This complements the previous work of the first and third authors regarding the existence and continuity of solutions with respect to parameters. In addition, we treat separately time scale dynamic equations which are linear with respect to the unknown function and the parameter. For this case we derive an improved result which says that the solution is an entire function of the parameter.
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