https://web.mst.edu/~bohner/papers/oaabotonrde.pdf

Oscillation and asymptotic behavior of third-order nonlinear retarded dynamic equations

https://web.mst.edu/~bohner/papers/ocfsodeots.pdf

Oscillation criteria for second-order dynamic equations on time scales

The purpose of this paper is to examine oscillatory properties of the third-order neutral delay differential equation . Some oscillatory and asymptotic criteria are presented. These criteria improve and complement those results in the literature. Moreover, some examples are given to illustrate the main results.

/pdf/oscillation-of-third-order-neutral-delay-differential-29nrk1oco8.pdf

Oscillation of Third-Order Neutral Delay Differential Equations

The study of half-linear differential equations has become an important area of research due to the fact that such equations occur in a variety of real-world problems such as in the study of \(p\)-Laplace equations, non-Newtonian fluid theory, and the turbulent flow of a polytrophic gas in a porous medium. On the basis of these background details, we study oscillatory behavior of a class of second-order neutral functional dynamic equations on a time scale. New criteria improve and complement related results reported in the literature. Some examples are included to illustrate the results obtained. In particular, an example regarding the second-order neutral differential equation is also provided to show that these theorems improve those in the continuous case.

https://www.emis.de/journals/BMMSS/pdf/acceptedpapers/2012-12-065-R1.pdf

Oscillation of Second-Order Nonlinear Neutral Dynamic Equations with Noncanonical Operators

This paper is concerned with oscillatory behavior of a class of fourth-order delay dynamic equations on a time scale. In the general time scales case, four oscillation theorems are presented that can be used in cases where known results fail to apply. The results obtained can be applied to an equation which is referred to as Swift-Hohenberg delay equation on a time scale. These criteria improve a number of related contributions to the subject. Some illustrative examples are provided.

/pdf/oscillation-of-fourth-order-delay-dynamic-equations-1xc9s7mmgv.pdf

Oscillation of fourth-order delay dynamic equations

The oscillation for certain third-order nonlinear neutral delay dynamic equations on time scales is discussed in this article. By using the generalized Riccati transformation and the inequality technique, three new different sufficient conditions which ensure that every solution is oscillatory or converges to zero are established. The results obtained essentially generalize and improve earlier ones.

Shou Hua Liu

Papers

Oscillation for Third-Order Nonlinear Delay Dynamic Equations on Time Scales