Advanced Studies in Pure Mathematics

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

Pavel Řehák

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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.

Article information

Source
Advances in Discrete Dynamical Systems, S. Elaydi, K. Nishimura, M. Shishikura and N. Tose, eds. (Tokyo: Mathematical Society of Japan, 2009), 261-269

Dates
Received: 12 October 2007
First available in Project Euclid: 28 November 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1543447659

Digital Object Identifier
doi:10.2969/aspm/05310261

Mathematical Reviews number (MathSciNet)
MR2582423

Zentralblatt MATH identifier
1182.39004

Subjects
Primary: 34C10: Oscillation theory, zeros, disconjugacy and comparison theory 39A11 39A12: Discrete version of topics in analysis 39A13: Difference equations, scaling ($q$-differences) [See also 33Dxx]

Citation

Řehák, Pavel. A Willett type criterion with the best possible constant for linear dynamic equations. Advances in Discrete Dynamical Systems, 261--269, Mathematical Society of Japan, Tokyo, Japan, 2009. doi:10.2969/aspm/05310261. https://projecteuclid.org/euclid.aspm/1543447659


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