Opuscula Math. 39, no. 1 (2019), 91-108

Opuscula Mathematica

Oscillation criteria for even order neutral difference equations

S. Selvarangam
S. A. Rupadevi
E. Thandapani
S. Pinelas

Abstract. In this paper, we present some new sufficient conditions for oscillation of even order nonlinear neutral difference equation of the form \[\Delta^m(x_n+ax_{n-\tau_1}+bx_{n+\tau_2})+p_nx_{n-\sigma_1}^{\alpha}+q_nx_{n+\sigma_2}^{\beta}=0,\quad n\geq n_0\gt0,\] where \(m\geq 2\) is an even integer, using arithmetic-geometric mean inequality. Examples are provided to illustrate the main results.

Keywords: even order, neutral difference equation, oscillation, asymptotic behavior, mixed type.

Mathematics Subject Classification: 39A10.

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Cite this article as:
S. Selvarangam, S. A. Rupadevi, E. Thandapani, S. Pinelas, Oscillation criteria for even order neutral difference equations, Opuscula Math. 39, no. 1 (2019), 91-108, https://doi.org/10.7494/OpMath.2019.39.1.91

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