Regular variation on time scales and dynamic equations

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Authors	ŘEHÁK Pavel
Year of publication	2008
Type	Article in Periodical
Magazine / Source	The Australian Journal of Mathematical Analysis and Applications
MU Faculty or unit	Faculty of Education
Citation
Field	General mathematics
Keywords	Time scale; Regularly varying function; Karamata function; Regularly varying sequence; Differential equation; Difference equation; Dynamic equation.
Description	The purpose of this paper is twofold. First, we want to initiate a study of regular variation on time scales by introducing this concept in such a way that it unifies and extends well studied continuous and discrete cases. Some basic properties of regularly varying functions on time scales will be established as well. Second, we give conditions under which certain solutions of linear second order dynamic equations are regularly varying. Open problems and possible directions for a future research are discussed, too.
Related projects:	Difference equations and dynamic equations on time scales II