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VOL. 53 | 2009 A Willett type criterion with the best possible constant for linear dynamic equations
Pavel Řehák

Editor(s) Saber Elaydi, Kazuo Nishimura, Mitsuhiro Shishikura, Nobuyuki Tose

Abstract

We establish oscillation criteria for the linear dynamic equation $(r(t)y^{\Delta})^{\Delta} + p(t) y^{\sigma} = 0$. 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 $p$, $r$, and primarily on the asymptotic behavior of graininess. In addition, we prove that the value of this new "constant" is the best possible.

Information

Published: 1 January 2009
First available in Project Euclid: 28 November 2018

zbMATH: 1182.39004
MathSciNet: MR2582423

Digital Object Identifier: 10.2969/aspm/05310261

Subjects:
Primary: 34C10, 39A11, 39A12, 39A13

Rights: Copyright © 2009 Mathematical Society of Japan

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