Oscillation Condition for First Order Non-Linear Delay Differential Equations with Deviating Arguments and Oscillatory Coefficients

Abstract

In this paper, we obtain a new oscillation condition for the first order non-linear delay differential equation of the form

  z^'(t) + q(t)f(z(τ(t))) = 0 ,     t ≥ t₀ > 0                                                       

where q and τ are continuous functions on [ t₀ ,∞), t₀ > 0, q(t) ≥  0 and  = ∞ and

 f ϵ C(R ,R ), τ(t) < t and zf(z) > 0 for z ≠ 0.Without imposing the nonnegative restriction on the coefficient functions q(t) a new sufficient oscillation criterion is obtained . An example illustrating the result is also given.