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December 2021 Oscillatory behavior of Nabla dynamic equations on time scales
Özkan Öcalan
Rocky Mountain J. Math. 51(6): 2185-2194 (December 2021). DOI: 10.1216/rmj.2021.51.2185

Abstract

Consider the first-order nabla dynamic equations

x(t)i=1mpi(t)x(τi(t))=0,t[t0,)𝕋,

where pi(t) (i=1,2,,m)Cld([t0,)𝕋,+), τi(t)(i=1,2,,m)Cld([t0,)𝕋,𝕋) and τi(t)t. Under the assumption that the τi(t) are not necessarily monotone (i=1,2,,m), we present new sufficient conditions for the oscillation of first-order nabla dynamic equations on time scales. We can say that this paper is the first in the literature in obtaining the oscillations of the solutions of the above equation. An example illustrating the results is also given.

Citation

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Özkan Öcalan. "Oscillatory behavior of Nabla dynamic equations on time scales." Rocky Mountain J. Math. 51 (6) 2185 - 2194, December 2021. https://doi.org/10.1216/rmj.2021.51.2185

Information

Received: 25 December 2020; Revised: 5 May 2021; Accepted: 8 May 2021; Published: December 2021
First available in Project Euclid: 22 March 2022

Digital Object Identifier: 10.1216/rmj.2021.51.2185

Subjects:
Primary: 34C10 , 34N05 , 39A12 , 39A21

Keywords: nabla dynamic equations , nonmonotone , oscillatory solutions , time scale

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.51 • No. 6 • December 2021
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