Necessary and sufficient conditions for the oscillation of delay differential equation with a piecewise constant argument

Abstract

The characteristic equation for an equation with continuous and piecewise constant argument in the form x˙(t)+px(t−τ)+qx([t−k])=0    where  p, q∈ℜ, τ∈ℜ+and  k∈ℵ is presented, which when q=0 reduces to f(λ)=λ+e−λτ=0 and when p=0 reduces to λ−1+qλ−k=0. Also, the necessary and sufficient conditions for oscillation are obtained.