Oscillatory and asymptotic behaviour of a neutral differential equation with oscillating coefficients

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 ...

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 ∞ ...

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

Oscillatory and Asymptotic Behaviour of Second Order Neutral Dynamic Equations with Positive and Negative Coefficients

In this paper, oscillatory and asymptotic properties of solutions of nonlinear second order neutral dynamic equations of the form ( r(t)(y(t)+ p(t)y(α(t)))Δ )Δ +q(t)G(y(β(t)))−h(t)H(y(γ(t))) = 0 and ( r(t)(y(t)+ p(t)y(α(t)))Δ )Δ +q(t)G(y(β(t)))−h(t)H(y(γ(t))) = f (t) are studied under assumptions

Oscillatory and Asymptotic Behaviour of a Homogeneous Neutral Delay Difference Equation of Second Order

In this paper we find sufficient conditions for every solution of the neutral delay difference equation ∆(rn∆(yn − pnyn−m)) + qnG(yn−k) = 0 to oscillate or to tend to zero or ±∞ as n → ∞, where ∆ is the forward difference operator given by ∆xn = xn+1−xn, pn, qn, and rn are infinite sequences of real numbers with qn ≥ 0, rn > 0. Different ranges of {pn} are considered. This paper improves,genera...