الفهرس | Only 14 pages are availabe for public view |
Abstract This thesis contains six chapters: Chapter 1 contains the basic concepts of the theory of functional differential equations and some preliminary results of the theory of second and third order neutral delay differential equations. In Chapter 2, we give an introduction to the theory of dynamic equations on time scales, differentiation, integration, and some examples of time scales. In Chapter 3, we establish some new oscillation criteria for second order nonlinear neutral delay dynamic equation with ”Maxima” of the form on a time scale T. The results of this chapter generalize and extend the results of [2, 4, 10, 33, 47, 51]. In Chapter 4, we introduce some new oscillation criteria for second order nonlinear neutral delay dynamic equation with nonpositive neutral term and ”Maxima” of the form on a time scale T. The current results not only improve and extend results of [14, 34, 42, 50], but also can be applied to some oscillation problems that are not covered before. In Chapter 5, the oscillatory and asymptotic behavior of the third order nonlinear neutral dynamic equation with ”Maxima” of the form on a time scale T is studied. Our results generalize and extend the results of [11, 12, 29]. Chapter 6 aims to utilize Riccati technique in studying the oscillation problem of the third order nonlinear neutral delay dynamic equation with ”Maxima” and mixed arguments of the form where on a time scale T. The present results are new and extend many known published results for oscillation of third order neutral differential, difference and dynamic equations (see [8,11–13,29,38,54]). At the end of this chapter, a counter example is given to illustrate the main theorem of M. Zingel and F. S. Topal [54] is not true. The correct formula for this theorem and related results in their work are given. |