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We derive oscillation criteria for general-type neutral differential equations [x(t) +αx(t− τ) +βx(t+ τ)] = δ bax(t − s)dsq1(t,s) + δ ∫ d c x(t + s)dsq2(t,s) = 0, t ≥ t0, where t0 ≥ 0, δ = ±1, τ > 0, b > a ≥ 0, d > c ≥ 0, α and β are real numbers, the functions q1(t,s) : [t0,∞)× [a,b]→R and q2(t,s) : [t0,∞)× [c,d]→R are nondecreasing in s for each fixed t,(More)
By using a Picone type formula in comparison with oscillatory unforced half-linear equations, we derive new oscillation criteria for second order forced super-half-linear impulsive differential equations having fixed moments of impulse actions. In the superlinear case, the effect of a damping term is also considered.
By means of Riccati transformation technique, we establish some new oscillation criteria for the third-order nonlinear delay dynamic equations x ∆ 3 (t) + p(t)x γ (τ (t)) = 0 on a time scale T unbounded above, here γ > 0 is a quotient of odd positive integers with p real-valued positive rd-continuous function defined on T. Three examples are given to(More)
To cite this Article Anderson, Douglas R. and Zafer, A.(2010) 'Interval criteria for second-order super-half-linear functional dynamic equations with delay and advance arguments', This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing,(More)
Recommended by Mariella Cecchi We obtain new oscillation criteria for second-order forced dynamic equations on time scales containing mixed nonlinearities of the form rtΦ α x Δ Δ ft, x σ et, t ∈ t 0 , ∞ T with ft, x qtΦ α x n i1 q i tΦ βi x, Φ * u |u| * −1 u, where t 0 , ∞ T is a time scale interval with t 0 ∈ T, the functions r, q, q i , e : t 0 , ∞ T → R(More)