ASYMPTOTIC BEHAVIOUR OF SECOND ORDER NEUTRAL DIFFERENTIAL EQUATIONS WITH "MAXIMA"

Oscillatory and Asymptotic Behavior of Solutions of Second Order Neutral Delay Differential Equations with “maxima”

The authors establish some new criteria for the oscillation and asymptotic behavior of all solutions of the equation. (a(t)(x(t) + p(t)x(τ(t)))) + q(t) max [σ(t),t] x(s) = 0, t ≥ t0 ≥ 0, where a(t) > 0, q(t) ≥ 0, τ(t) ≤ t, σ(t) ≤ t, α is the ratio of odd positive integers, and ∫∞ 0 dt a(t) < ∞. Examples are included to illustrate the results. AMS Subject Classification: 34K11, 34K99

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

Oscillation and Asymptotic Behaviour of Solutions of Second Order Neutral Differential Equations with Positive and Negative Coefficients

Sufficient conditions in terms of the coefficient functions for the oscillation and asymptotic behavior of nonoscillatory solutions of a class of second order nonlinear neutral differential equations have been obtained. The results improve some earlier results.

Asymptotic stability and asymptotic solutions of second-order differential equations

We improve, simplify, and extend on quasi-linear case some results on asymptotical stability of ordinary second-order differential equations with complex-valued coefficients obtained in our previous paper [G.R. Hovhannisyan, Asymptotic stability for second-order differential equations with complex coefficients, Electron. J. Differential Equations 2004 (85) (2004) 1–20]. To prove asymptotic stab...

The Asymptotic Behavior for Second-Order Neutral Stochastic Partial Differential Equations with Infinite Delay