Necessary and sufficient condition for oscillations of neutral differential equations

Abstract

Abstract Consider the neutral delay differential equation where p ∈ R , τ ≥ 0, q 1 > 0, σ 1 ≥ 0, for i = 1, 2, …, k . We prove the following result. Theorem. A necessary and sufficient condition for the oscillation of all solutions of Eq. (1) is that the characteristic equation has no real roots .