2 School of Mathematics The University of New South Wales, Sydney NSW 2052, Australia Abstract:We consider a boundary value problem (BVP) for systems of second-order dynamic equations on time scales. Using methods involving dynamic inequalities, we formulate conditions under which all solutions to a certain family of systems of dynamic equations satisfy certain a priori bounds. These results ar...

In this paper, we present some asymptotic results related to the scalar dynamic equation with a delayed argument. Using the time scale calculus we generalize some results known in the differential and difference case to the more general dynamic case.

We obtain oscillation criteria for a second order self-adjoint matrix differential equation on a measure chain in terms of the eigenvalues of the coefficient matrices and the graininess function. We illustrate our results with some nontrivial examples.

Wewill establish some oscillation criteria for the third-order Emden-Fowler neutral delay dynamic equations r t x t − a t x τ t ΔΔ Δ p t x δ t 0 on a time scale T, where γ > 0 is a quotient of odd positive integers with r, a, and p real-valued positive rd-continuous functions defined on T. To the best of our knowledge nothing is known regarding the qualitative behavior of these equations on tim...

and Applied Analysis 3 Theorem 2.9 see 27 . If f, g ∈ T,R , and t ∈ T, then i

We give a proposal to generalize the concept of the differential equations on time scales [1, 2, 3], such that they can be more appropriate for the analysis of real world problems, and give more opportunities to increase the theoretical depth of investigation.

In this article, we study the oscillation of second order impulsive dynamic equations on time scales. The effect of the moments of impulse are fixed. Using Riccati transformation techniques, we obtain some conditions for the oscillation of all solutions

In this paper, we will establish some oscillation criteria for the higher order linear dynamic equation on time scale in term of the coefficients and the graininess function. We illustrate our results with an example.

In this paper, we consider the system of boundary value problems for higherdimensional dynamic equations on time scales. We establish criteria for the existence of at least one or two positive solutions. We shall also obtain criteria which lead to nonexistence of positive solutions. Examples applying our results are also given.