Oscillations for Nonlinear Neutral Delay Differential Equations with Variable Coefficients

An Approximate Method for System of Nonlinear Volterra Integro-Differential Equations with Variable Coefficients

In this paper, we apply the differential transform (DT) method for finding approximate solution of the system of linear and nonlinear Volterra integro-differential equations with variable coefficients, especially of higher order. We also obtain an error bound for the approximate solution. Since, in this method the coefficients of Taylor series expansion of solution is obtained by a recurrence r...

EXISTENCE OF PERIODIC SOLUTIONS IN TOTALLY NONLINEAR NEUTRAL DIFFERANCE EQUATIONS WITH VARIABLE DELAY

Periodic Solutions for Third-order Nonlinear Delay Differential Equations with Variable Coefficients

In this paper, the following third-order nonlinear delay differential equation with periodic coefficients x′′′(t) + p(t)x′′(t) + q(t)x′(t) + r(t)x(t) = f (t, x (t) , x(t− τ(t))) + d dt g (t, x (t− τ (t))) , is considered. By employing Green’s function, Krasnoselskii’s fixed point theorem and the contraction mapping principle, we state and prove the existence and uniqueness of periodic solutions...

On the One-Leg Methods for Solving Nonlinear Neutral Differential Equations with Variable Delay

Based on A-stable one-leg methods and linear interpolations, we introduce four algorithms for solving neutral differential equations with variable delay. A natural question is which algorithm is better. To answer this question, we analyse the error behavior of the four algorithms and obtain their error bounds under a one-sided Lipschitz condition and some classical Lipschitz conditions. After e...

Oscillation Results of Higher Order Nonlinear Neutral Delay Differential Equations with Oscillating Coefficients

In this paper, we shall consider higher order nonlinear neutral delay differential equation of the type [x(t) + p(t)x(τ(t))] + q(t) [x(σ(t))] = 0, t ≥ t0, n ∈ N, (*) where p ∈ C ([t0,∞) ,R) is oscillatory and lim t→∞ p(t) = 0, q ∈ C ( [t0,∞) ,R ) , τ, σ ∈ C ([t0,∞) ,R), τ(t), σ(t) < t, lim t→∞ τ(t) = lim t→∞ σ(t) =∞ and α ∈ (0,∞) is a ratio of odd positive integers. If α ∈ (0, 1), equation (*) ...