Title: Oscillatory and stability of a mixed type difference equation with variable coefficients

Authors: Sandra Pinelas; Nedjem Eddine Ramdani; Ali Fuat Yeniçerioglu; Yubin Yan

Addresses: RUDN University, 6 Miklukho-Maklaya St., Moscow, 117198, Russia ' Department of Civil Engineering, University of Saad Dahleb Blida, 1, Blida, Algeria ' Kocaeli University, Faculty of Education, Kocaeli, 41380, Turkey ' Department of Mathematical and Physical Sciences, University of Chester, Chester, CH1 4BJ, UK

Abstract: The goal of this paper is to study the oscillatory and stability of the mixed type difference equation with variable coefficients ∆x(n) = ℓ ∑ i=1 p_i(n)x(τ_i(n)) + m ∑ j=1 q_j(n)x(σ_i(n)), n ≥ n₀, where τ_i(n) is the delay term and σ_j(n) is the advance term and they are positive real sequences for i = 1, . . . , l and j = 1, . . . , m, respectively, and p_i(n) and q_j(n) are real functions. This paper generalises some known results and the examples illustrate the results.

Keywords: mixed type difference equation; asymptotic behaviour; stability; characteristic equation; oscillatory solutions; solution; numerical solutions; variable coefficients.

DOI: 10.1504/IJDSDE.2021.117364

International Journal of Dynamical Systems and Differential Equations, 2021 Vol.11 No.3/4, pp.391 - 421

Received: 21 May 2020
Accepted: 04 Dec 2020
Published online: 01 Sep 2021 *

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