By means of Mawhin’s continuation theorem, we study a kind of third-order p-Laplacian functional differential equation with distributed delay in the form: ( φp(x ′(t)) )′′ = g ( t, ∫ 0 −τ x(t+ s) dα(s) ) + e(t), some criteria to guarantee the existence of periodic solutions are obtained. Keywords—p–Laplacian, Distributed delay, Periodic solution, Mawhin’s continuation theorem

In this article, we obtain oscillation conditions for second-order differential equation with neutral term. Our results extend, improve, and simplify some known delay equations. Several effective illustrative implementations are provided.

By using the averaging technique, some integral oscillation criteria are obtained for even order damped delay differential equations. 1 – Introduction This paper deals with the oscillatory behavior of the even order damped delay differential equation (1.1) ( Φ(xn−1)(t)) )′ + p(t)Φ(x(n−1)(t)) + f ( t, x[ τ01(t) ], ..., x[ τ0m(t) ], ..., x(n−1)[ τn−11(t) ], ..., x (n−1)[ τn−1m(t) ] ) = 0 for t ≥ ...

We establish some new criteria for the oscillation of second-order Emden–Fowler neutral delay differential equations.We study the case of superlinear and the case of sublinear equations subject to various conditions. The results obtained show that the presence of a neutral term in a differential equation can cause or destroy oscillatory properties. Several examples are provided to illustrate th...