A necessary and sufficient condition for the oscillation of neutral equations

AbstractConsider the neutral differential equation ddt [y(t) + py(t − τ)] + qy(t − σ) = 0, t ≧ t0 (∗) where p, q, τ, and σ are real numbers. Then a necessary and sufficient condition for the oscillation of (∗) is that the characteristic equation λ + pλe−λτ + qe−λσ = 0 has no real roots