Yibing Sun

Oscillation of Second-Order Neutral Functional Differential Equations with Mixed Nonlinearities

We study the following second-order neutral functional differential equation with mixed nonlinearities (??(??)|(??(??)

Oscillation Criteria for Second-Order Quasilinear Neutral Delay Dynamic Equations on Time Scales

We establish some new oscillation criteria for the second-order quasilinear neutral delay dynamic equations on a time scale , where , . Our results generalize and improve some known results for oscillation of second-order nonlinear delay dynamic equations on time scales. Some examples are considered to illustrate our main results.

Oscillation criteria for p-Laplacian delay dynamic equations with damping on time scales

AbstractIn this paper, we establish some new oscillation criteria for p-Laplacian delay dynamic equations with damping (a(t)Φ(xΔ(t)))Δ+p(t)Φ(xΔ(t))+q(t)f(Φ(x(τ(t))))=0 on a time scale T, here Φ(s)=|s|γ−2s, γ>1 with a, p and q are positive real-valued rd-continuous functions defined on T. By using the Riccati transformation technique and integral averaging technique, some new sufficient conditions, which ensure that every solution oscillates, are established. Our results in this paper not only extend and improve the known results, but also unify the results about oscillation criteria for p-Laplacian delay differential equations with damping and p-Laplacian delay difference equations with damping.MSC:34C10, 34K11, 39A21.

Interval Oscillation Criteria for Second-Order Nonlinear Forced Dynamic Equations with Damping on Time Scales

By using the Riccati transformation technique and constructing a class of Philos-type functions on time scales, we establish some new interval oscillation criteria for the second-order damped nonlinear dynamic equations with forced term of the form on a time scale which is unbounded, where is a quotient of odd positive integer. Our results in this paper extend and improve some known results. Some examples are given here to illustrate our main results.

Oscillation Criteria for Certain Even Order Neutral Delay Differential Equations with Mixed Nonlinearities

We establish some oscillation criteria for the following certain even order neutral delay differential equations with mixed nonlinearities: where is even integer, and Our results generalize and improve some known results for oscillation of certain even order neutral delay differential equations with mixed nonlinearities.

Oscillation theorem for second order delay dynamic equations on time scales with mixed nonlinearities

By means of Riccati transformation technique and inequalities, the oscillation criteria for second order delay dynamic equations on time scales with mixed nonlinearities are studied. Two sufficient conditions are obtained for oscillation of this equation. The results in this paper extend and improve some known results for the corresponding equations with mixed nonlinearities.