A Willett type criterion with the best possible constant for linear dynamic equations

0329935 - MÚ 2010 RIV JP eng J - Journal Article
Řehák, Pavel
A Willett type criterion with the best possible constant for linear dynamic equations.
[Kritérium Willettova typu s nejlepší konstantou pro lineární dynamické rovnice.]
Advances in Discrete Dynamical Systems. vol. 53, - (2009), s. 261-269. ISBN 978-4-931469-49-5. ISSN 1793-4338.
[11th International Conference on Difference Equations and Applications. Kyoto, 24.07.2006-28.07.2006]
R&D Projects: GA AV ČR KJB1019407
Institutional research plan: CEZ:AV0Z10190503
Keywords : Willett criterion * linear dynamic equation * time scale
Subject RIV: BA - General Mathematics

We establish oscillation criteria a the linear dynamic equation. These criteria can be understood as an extension of the classical Willett criterion. What is special on these new results is that the constant involved in the criteria, which is equal to the magic 1/4 in the differential equations case, is in fact no more constant. In general case, it depends on the asymptotic behavior of the coefficients, and primarily on the asymptotic behavior of graininess. In addition, we prove that the value of this new constant is the best possible.

Jsou odvozena kritéria Willettova typu pro lineární dynamické rovnice. Je ukázáno, že konstanta 1/4 známá ze spojité teorie může mít odlišnou hodnotu, která závisí na koeficientech rovnice a zrnitosti. je ukázáno, že tato nová konstanta je nejlepší možná.
Permanent Link: http://hdl.handle.net/11104/0175833