We study the existence of periodic solutions of the second order nonlinear neutral differential equation with variable delay x′′ (t) + p (t)x′ (t) + q (t)h (x (t)) = c (t)x′ (t− τ (t)) + f (t, x (t− τ (t))) . We invert the given equation to obtain an integral, but equivalent, equation from which we define a fixed point mapping written as a sum of a large contraction and a compact map. We show t...

In the present paper, the mathematical model of a test case central heating system is developed in the form of a nonlinear neutral time delay model which in turn is simplified to a neutral time delay model with constant time delay. In the process it is shown that the influence of the delay is significant, thus its incorporation to the model is of high importance. A PI controller is derived to c...

With the development of modern society, research on properties of ordinary differential equation is becoming one of the hotspots in mathematical field. Neutral differential equation which is usually generated in natural science and engineering field is always extensively concerned by many scientific researchers for it can effectively describe multiple complex phenomena in natural world. In rece...

In this work, we use the generalized Riccati transformation and the inequality technique to establish some new oscillation criteria for the second-order nonlinear delay dynamic equation p t xΔ t γ Δ q t f x τ t 0, on a time scale T, where γ is the quotient of odd positive integers and p(t) and q(t) are positive right-dense continuous rd-continuous functions on T. Our results improve and extend ...