A new oscillation result for nonlinear differential equations with nonmonotone delay

OpenAlex İngilizce

In this article, our objective is to study the oscillation of first order nonlinear delay differential equationx (t) + p(t) f (x(τ(t))) = 0, t ≥ t 0 , where the functions p(t) and τ(t) are functions of nonnegative real numbers, τ(t) is not necessarily monotone such that τ(t) ≤ t for t ≥ t 0 , lim t→∞ τ(t) = ∞, f ∈ C(R, R) and x f (x) > 0 for x = 0. Also, we establish a new oscillation condition involving both limsup and liminf.Finally, we present two examples to demonstrate the main result.