Necessary and sufficient conditions for oscillations of first order neutral delay difference equations with constant coefficients - Murugesan, A.; Sowmiya, P. (International Journal of Advanced Mathematical Sciences, 2015)
In this paper, we establish the necessary and sufficient conditions for oscillation of the following first order neutral delay difference equationÂ equation* Δ[x(n)+px(n-τ)]+qx(n-σ)=0, n≥ n_0, (*) equation*where \(τ\) and \(σ\) are positive integers, \(p eq 0\) is a real number and \(q\) is a positive real number. We proved that every solution of (*) oscillates if and only if its characteristic equationequation*(λ-1)(1+pλ^-τ)+qλ^-σ=0(**) equation*has no positive roots.