In this paper, we investigate comparison criteria for third order nonlinear dynamic equations with mixed nonlinearities on time scales. Our results are essentially new. Some applications illustrating the importance of our results are included and these applications solve a problem posed in [2, Remark 3.3].

In this paper, we establish some new oscillation criteria for the third order nonlinear delay dynamic equations

We consider a general class of discrete-space linear partial dynamic equations. The basic properties of solutions are provided (existence and uniqueness, sign preservation, maximum principle). Above all, we derive the following main results: first, we prove that the solutions depend continuously on the choice of the time scale. Second, we show that, under certain conditions, the solutions descr...

In certain situations, observations are collected on a multivariate time series at a certain temporal scale. However, there may also exist underlying time series behavior on a larger temporal scale that is of interest. Often times, identifying the behavior of the data over the course of the larger scale is the key objective. Because this large scale trend is not being directly observed, describ...

In this paper, we study the oscillation of a class of second-order nonlinear neutral damped variable delay dynamic equations on time scales. By using a generalized Riccati transformation technique, we obtain some sufficient conditions for the oscillation of the equations. The results of this paper improve and extend some known results. We also illustrate our main results with some examples. Key...

This paper deals with solutions of diffusion-type partial dynamic equations on discrete-space domains. We provide two methods for finding explicit solutions, examine their asymptotic behavior and time integrability. These properties depend significantly not only on the underlying time structure but also on the dimension and symmetry of the problem. Throughout the paper, the results are interpre...

We are concerned with the asymptotic behavior of solutions of an nth order linear dynamic equation on a time scale in terms of Taylor monomials. In particular, we describe the asymptotic behavior of the so-called (first) principal solution in terms of the Taylor monomial of degree n−1. Several interesting properties of the Taylor monomials are established so that we can prove our main results.

In this paper we will establish some oscillation criteria for the second-order nonlinear neutral delay dynamic equation ( r(t) (( y(t)+ p(t)y(t − τ))∆)γ )∆ + f (t, y(t − δ))= 0 on a time scale T; here γ > 0 is a quotient of odd positive integers with r(t) and p(t) real-valued positive functions defined on T. To the best of our knowledge nothing is known regarding the qualitative behavior of the...