International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 3, Pages 493-497
doi:10.1155/S0161171298000702
Necessary and sufficient conditions for the oscillation of delay differential equations with a piecewise constant argument
H.A. Agwo
Department of Mathematics, Faculty of Education, Ain Shams University, Roxy , Cairo, Egypt
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.