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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.

Stability criteria are given for linear periodic Hamiltonian systems with impulse effect. A Lyapunov type inequality and a disconjugacy criterion are also established. The results improve the ones in the literature for such systems.

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

Interval oscillation criteria are established for second-order forced delay dynamic equations on time scales containing mixed nonlinearities of the form r(t)Φ α (x ∆ (t)) ∆ + p 0 (t)Φ α (x(τ 0 (t))) + n i=1 p i (t)Φ β i (x(τ i (t))) = e(t), t ∈ [t 0 , ∞) T where T is a time scale, t 0 ∈ T a fixed number; [t 0 , ∞) T is a time scale interval; Φ * (u) = |u| *… (More)