Electron. J. Diff. Equ., Vol. 2015 (2015), No. 128, pp. 1-14.

Oscillation criteria for even-order nonlinear neutral difference equations with continuous variables

Shuhui Wu, Pargat Singh Calay, Zhanyuan Hou

Abstract:
In this article, we study the oscillatory behavior of solutions to even-order nonlinear neutral difference equations of the form
$$ \Delta^m_\tau( x(t)-px(t-r))+f(t,x(g(t)))=0. $$
Using an integral transformation, the Riccati transformation, and iteration, we obtain sufficient conditions for all solutions to be oscillatory. Examples are also given to illustrate the obtained criteria.

Submitted November 2, 2014. Published May 7, 2015.
Math Subject Classifications: 39A10, 39A21.
Key Words: Neutral difference equations; oscillation; continuous variable.

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Shuhui Wu
School of Science
Zhejiang University of Science and Technology
318 Liuhe Road, Hangzhou 310023, China
email: s.wu@zust.edu.cn, shuhui75@hotmail.com
Pargat Singh Calay
Faculty of Computing
London Metropolitan University
166--220 Holloway Road, London N7 8DB, UK
email: p.calay@londment.ac.uk
  Zhanyuan Hou
Faculty of Computing
London Metropolitan University
166--220 Holloway Road, London N7 8DB, UK
email: z.how@londonmet.ac.uk

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