Geodesic
Oscillation criteria for even-order nonlinear neutral difference equations with continuous variables
Electronic Journal of Differential Equations, Tome 2015 (2015).

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Summary: 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.
Classification : 39A10, 39A21
Keywords: neutral difference equations, oscillation, continuous variable 
@article{EJDE_2015__2015__a79,
     author = {Wu, Shuhui and Calay, Pargat Singh and Hou, Zhanyuan},
     title = {Oscillation criteria for even-order nonlinear neutral difference equations with continuous variables},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2015},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a79/}
}
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Wu, Shuhui; Calay, Pargat Singh; Hou, Zhanyuan. Oscillation criteria for even-order nonlinear neutral difference equations with continuous variables. Electronic Journal of Differential Equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a79/