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Oscillation and nonoscillation criteria for second-order nonlinear difference equations of Euler type


Author: Naoto Yamaoka
Journal: Proc. Amer. Math. Soc. 146 (2018), 2069-2081
MSC (2010): Primary 39A21; Secondary 39A12
DOI: https://doi.org/10.1090/proc/13888
Published electronically: December 11, 2017
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Abstract: This paper deals with the oscillatory behavior of solutions of difference equations corresponding to second-order nonlinear differential equations of Euler type. The obtained results are represented as a pair of oscillation and nonoscillation criteria, and are best possible in a certain sense. Linear difference equations corresponding to the Riemann-Weber version of the Euler differential equation and its extended equations play an important role in proving our results. The proofs of our results are based on the Riccati technique and the phase plane analysis of a system.


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Additional Information

Naoto Yamaoka
Affiliation: Department of Mathematical Sciences, Osaka Prefecture University, Sakai 599-8531, Japan
Email: yamaoka@ms.osakafu-u.ac.jp

DOI: https://doi.org/10.1090/proc/13888
Keywords: Cauchy-Euler equation, oscillation constant, logarithm functions, Riccati technique, phase plane analysis.
Received by editor(s): April 6, 2017
Received by editor(s) in revised form: July 7, 2017
Published electronically: December 11, 2017
Communicated by: Mourad Ismail
Article copyright: © Copyright 2017 American Mathematical Society

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