Oscillation Tests for Linear Difference Equations with Non-Monotone Arguments

Abstract

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],\[\Delta x(n) + p(n)x(\tau (n)) = 0,\,n \in {_0}\quad [\nabla x(n) - q(n)x(\sigma (n)) = 0,\,n \in ],\ , 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\[{(\tau (n))_{n \ge 0}},\quad {(\sigma (n))_{n \ge 1}}\] are (not necessarily 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.