New oscillation criteria for second-order delay differential equations with mixed nonlinearities

We establish new oscillation criteria for second-order delay differential equations with mixed nonlinearities of the form p t x t n i 1 p i t x t−τ i n i 1 q i t |x t−τ i | αi sgn x t−τ i e t , t ≥ 0, where p t , p i t , q i t , and e t are continuous functions defined on 0, ∞ , and p t > 0, p t ≥ 0, and No restriction is imposed on the potentials p i t , q i t , and e t to be nonnegative. These oscillation criteria extend and improve the results given in the recent papers. An interesting example illustrating the sharpness of our results is also provided

Interval Oscillation Criteria for Second-Order Forced Functional Dynamic Equations on Time Scales

This paper is concerned with oscillation of second-order forced functional dynamic equations of the form (r(t)(xΔ(t))γ)Δ+∑i=0n‍qi(t)|x(δi(t))|αisgn  x(δi(t))=e(t) on time scales. By using a generalized Riccati technique and integral averaging techniques, we establish new oscillation criteria which handle some cases not covered by known criteria