الفهرس 
Calculus on Time Scalesيوجد فقط 14 صفحة متاحة للعرض العام
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المستخلص
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.