OSCILLATION TESTS FOR LINEAR DIFFERENCE EQUATIONS WITH NON-MONOTONE ARGUMENTS

Abstract

This paper presents sufficient conditions involving limsup for the oscillation of all solutions of linear difference equations with general deviating argument of the form

Δx(n)+p(n)x(τ(n))=0, n∈ℕ₀ [∇x(n)-q(n)x(σ(n))=0, n∈ℕ],

where (p(n))_{n≥0} and (q(n))_{n≥1} are sequences of nonnegative real numbers and (τ(n))_{n≥0}, (σ(n))_{n≥1} are (not neccesarily monotone) sequences of integers. The results obtained improve all well-known results existing in the literature and an example, numerically solved in MATLAB, illustrating the significance of these results is provided.