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New oscillation criteria are established for second-order differential equations containing both delay and advanced arguments of the form, (k(t) x'(t))'

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)

New oscillation and nonoscillation criteria are established for second order linear equations with damping and forcing terms. Examples are given to illustrate the results.

- Douglas R. Andersona, A. Zaferb, Douglas R. Anderson, A. Zafer
- 2010

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)