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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Oscillation and nonoscillation criteria for second-order nonlinear difference equations of Euler type
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by Naoto Yamaoka PDF
Proc. Amer. Math. Soc. 146 (2018), 2069-2081 Request permission


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
  • MR Author ID: 688560
  • Email:
  • 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
  • © Copyright 2017 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 146 (2018), 2069-2081
  • MSC (2010): Primary 39A21; Secondary 39A12
  • DOI:
  • MathSciNet review: 3767358