Asymptotic Behavior for Linear Delay-Differential Equations with Periodically Oscillatory Coefficients

Oscillatory and Asymptotic Behavior of Fourth Order Nonlinear Neutral Delay Differential Equations with Positive and Negative Coefficients

In this paper, Oscillatory and asymptotic behaviour of solutions of a class of nonlinear fourth order neutral differential equations with positive and negative coefficients of the form (H) (r(t)(y(t) + p(t)y(t− τ))′′)′′ + q(t)G(y(t− α)) − h(t)H(y(t− β)) = 0 and (NH) (r(t)(y(t) + p(t)y(t− τ))′′)′′ + q(t)G(y(t− α)) − h(t)H(y(t− β)) = f(t) are studied under the assumption ∫ ∞

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

Asymptotic behavior of impulsive neutral delay differential equations with positive and negative coefficients of Euler form

Asymptotic and Oscillatory Behavior of Higher Order Quasilinear Delay Differential Equations

In the paper, we offer such generalization of a lemma due to Philos (and partially Staikos), that yields many applications in the oscillation theory. We present its disposal in the comparison theory and we establish new oscillation criteria for n−th order delay differential equation (E) ` r(t) ˆ x ′(t) ̃ γ ́(n−1) + q(t)xγ(τ (t)) = 0. The presented technique essentially simplifies the examination...

Oscillatory Solutions for Certain Delay-differential Equations

The existence of oscillatory solutions for a certain class of scalar first order delay-differential equations is proved. An application to a delay logistic equation arising in certain models for population variation of a single specie in a constant environment with limited resources for growth is considered. It is known (cf. [1, 2]) that all solutions of the delay logistic equations (1) N'(t) =...