STABILITY CRITERIA FOR CERTAIN SECOND ORDER NEUTRAL DELAY DIFFERENTIAL EQUATIONS

In this paper we study the asymptotic stability of the zero solution of second order neutral delay differential equation of the form

                                                 y ′′(t) + αy′′(t − τ) + ay′ (t) + by′ (t − τ) + cy(t) + dy(t − τ) = 0,

where a, b, c, d, α ∈ (−1, 0)∪(0, 1), and τ > 0 are constants. In this paper, we obtain a new necessary condition and obtain robust method of determining whether the zero solution is asymptotically stable. In proving our results we make use of Pontryagin’s theory for quasi-polynomials.