الفهرس 
Preliminary Results for Oscillation of the Dynamic EquationsOnly 14 pages are availabe for public view
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Abstract
Summary
It is well known that, the differential equations fined a wide range of applications in biology, physics, social, engineering and other areas. The fundamental problem in the theory of differential equations is to deduce the qualitative properties of the solutions of a given equation from the analytic form of the equation because the nonintegrability of the equation makes the problem of obtaining solutions of differential equations in terms of the elementary functions of analysis not solvable for most equations. The oscillation theory of differential equations as a part of qualitative properties are very important for applications.
In the recent years, there has been increasing interest in obtaining sufficient conditions for the oscillation and nonoscillation of various equations on time-scales. So, it is the focus of our study.
The thesis consists of four chapters:
In Chapter 1, we state some basic definitions and theorems that will be used throughout the next chapters. Also, we introduce the time scales calculus. Finally, we mention some of the related results with our work.
In Chapter 2, we are concerned with the oscillatory behavior of forced second order functional differential equations with -Laplacian, damping and mixed nonlinearities on the form of
where , , is strictly increasing such that with ; with on ; ; and is nondecreasing. The function is such that , for Our interest is to establish oscillation criteria for above equation without assuming that , , , and are definition of sign. Also, illustrative example of our results is presented.
Our Results in this Chapter have been published in Serdica Math. J. 40, (2014), 55-76.
In Chapter 3, we are concerned with the oscillatory behavior of the second order nonlinear functional dynamic equation with -Laplacian, damping and nonlinearities given by Riemann-Stieltjes integrals
on a time scale which is unbounded above, where and for is strictly increasing with and is a time scale; and is nondecreasing; and are positive continuous functions on ; and , are nonnegative continuous functions on and with ; the functions and are continuous functions such that and for .
Both of the two cases
are considered.
The obtained results in this Chapter have been published in Mediterr. J. Math., 13, (2016), 981-1003.
In Chapter 4, we are concerned with the oscillation of solutions of third order nonlinear functional neutral dynamic equation of the form
on an above-unbounded time scale , where ; , ; , , are positive continuous functions on with such that
Our results extended and improve some known results for oscillation of third order nonlinear functional neutral dynamic equation. Some our results are illustrated by examples.