Oscillation of functional differential equations

Oscillation of Third-order Functional Differential Equations

The aim of this paper is to study oscillatory and asymptotic properties of the third-order nonlinear delay differential equation (E) ˆ a(t) ˆ x ′′(t) ̃ γ ̃ ′ + q(t)f(x [τ (t)]) = 0. Applying suitable comparison theorems we present new criteria for oscillation or certain asymptotic behavior of nonoscillatory solutions of (E). Obtained results essentially improve and complement earlier ones. Variou...

The oscillation of perturbed functional differential equations

we provide new oscillation criteria for the perturbed functional differential equations. This solves some open problems of [l]. An application to an equation arising in nonlinear neural networks is illustrated. @ 2000 Elsevier Science Ltd. All rights reserved. Keywords-Oscillation, Perturbed equation, Nonlinear neural networks

Oscillation Criteria for Functional Differential Equations

Consider the first-order linear delay differential equation x′(t) + p(t)x(τ(t)) = 0, t ≥ t0, and the second-order linear delay equation x′′(t) + p(t)x(τ(t)) = 0, t ≥ t0, where p and τ are continuous functions on [t0,∞), p(t) > 0, τ(t) is nondecreasing, τ(t) ≤ t for t ≥ t0 and limt→∞ τ(t) = ∞. Several oscillation criteria are presented for the first-order equation when

Oscillation of Volterra Integral Equations and Forced Functional Differential Equations

Random fractional functional differential equations

In this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the Lipschitz type condition. Moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.