Oscillatory Behaviour of a Higher Order Nonlinear Neutral Delay Type Functional Differential Equation with Oscillating Coefficients

Oscillation and Asymptotic Behaviour of a Higher-Order Nonlinear Neutral-Type Functional Differential Equation with Oscillating Coefficients

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 (*) ...

Unbounded oscillation of higher-order nonlinear delay dynamic equations of neutral type with oscillating coefficients

In this paper, we present a criterion on the oscillation of unbounded solutions for higher-order dynamic equations of the following form: [ x(t) +A(t)x(α(t)) ]∆n +B(t)F (x(β(t))) = φ(t) for t ∈ [t0,∞)T, (?) where n ∈ [2,∞)Z, t0 ∈ T, sup{T} = ∞, A ∈ Crd([t0,∞)T,R) is allowed to alternate in sign infinitely many times, B ∈ Crd([t0,∞)T,R), F ∈ Crd(R,R) is nondecreasing, and α, β ∈ Crd([t0,∞)T,T) a...

Sufficient Conditions for Oscillatory Behaviour of a First Order Neutral Difference Equation with Oscillating Coefficients

In this paper, we obtain sufficient conditions so that every solution of neutral functional difference equation ∆(yn − pnyτ(n)) + qnG(yσ(n)) = fn oscillates or tends to zero as n → ∞. Here ∆ is the forward difference operator given by ∆xn = xn+1−xn, and pn, qn, fn are the terms of oscillating infinite sequences; {τn} and {σn} are non-decreasing sequences, which are less than n and approaches ∞ ...

Oscillatory and Asymptotic Behaviour of a Neutral Differential Equation with Oscillating Coefficients

In this paper, we obtain sufficient conditions so that every solution of y(t) − n i=1 p i (t)y(δ i (t)) + m i=1 q i (t)y(σ i (t)) = f (t) oscillates or tends to zero as t → ∞. Here the coefficients p i (t), q i (t) and the forcing term f (t) are allowed to oscillate; such oscillation condition in all coefficients is very rare in the literature. Furthermore, this paper provides an answer to the ...