Oscillation Criteria for First Order Non-Linear Delay Differential Equations Caused by Non-Monotone Arguments

Abstract

This paper is concerned with the oscillatory behaviour of first – order nonlinear delay differential equation with variable non-monotone deviating arguments and nonnegative coefficients of the form, z^'(t) + p(t)f(z(τ(t)) = 0, τ(t) < t, t ≥ t₀ > 0_, where p and τ are continuous on [ t₀, ∞), p(t) ≥ 0 and  = ∞ and f ϵ C(R,R) and zf(z) >0 for z ≠ 0.Sufficient oscillation conditions involving limit superior and limit inferior  are obtained . An example, numerically solved, is also given to illustrate the applicability and strength of the obtained results over known ones.