Opuscula Math. 39, no. 1 (2019), 91-108
https://doi.org/10.7494/OpMath.2019.39.1.91

Opuscula Mathematica

Oscillation criteria for even order neutral difference equations

S. Selvarangam
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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• S. Selvarangam
• Department of Mathematics, Presidency College Chennai - 600 005, India
• Department of Mathematics, Presidency College Chennai - 600 005, India
• E. Thandapani
• University of Madras, Ramanujan Institute for Advanced Study in Mathematics, Chennai - 600 005, India
• Communicated by Marek Galewski.
• Revised: 2018-07-07.
• Accepted: 2018-07-07.
• Published online: 2018-08-07.