الفهرس 
1 PreliminariesOnly 14 pages are availabe for public view
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Abstract
Chapter 1 contains the basic concepts of theory of functional differential equations and some preliminary results of the oscillation theory of second order impulsive differ- ential equations.
In Chapter 2, An introduction to theory of dynamic equations on time scales, dif- ferentiation, integration and various properties of the exponential function on arbitrary time scale are added. Furthermore, the most important studies for the oscillation the- ory of second order impulsive dynamic equations on time scales are presented.
In Chapter 3, Some new oscillation criteria for the second-order nonlinear impulsive delay dynamic equation
〖(r(t〖)|x^∆ (t)|〗^(α-1) x^∆ (t))〗^∆+p(t)f(x(τ(t)))=0,t≠θ_k,k=1,2,…
∆(r(t〖)|x^∆ (t)|〗^(α-1) x^∆ (t))_(t=θ_k )+b_k f(x(τ(θ_k)))=0,t=θ_(k
on a time scale 𝕋 are established. Our results generalize and extend some pervious re- sults [13, 36, 38, 40] and can be applied to some oscillation problems that not discussed before. These results extend the known results for the dynamic equations with and
without impulses.
These results of this chapter are published in:
Electronic Journal of Mathematical Analysis and Applications, accepted. [4].
In Chapter 4, The Riccati transformation technique is utilized to establish some new oscillation criteria for the second-order nonlinear impulsive dynamic equation with damping term〖(r(t〖)(x^∆ (t))〗^α)〗^∆+q(t)〖)(x^∆ (t))〗^α+f(t,x^σ (t))=0,t≠θ_k
x(t_k^+ )=g_k (x(t_k^- )),x(t_k^+ )=h_k (x(t_k^- )),k=1,2,…
x(t_0^+ )=x_0,x^∆ (t_0^+ )=x_0^∆
on a time scale 𝕋, where α is the quotient of odd positive integers. Our results gen- eralize and extend some pervious results [17, 18, 19, 20] and can be applied to some oscillation problems that not discussed before.
These results of this chapter are published in:
Acta Mathematica Universitatis Comenianae, 88 (2019), 1-16. [3].
In Chapter 5, Some new oscillation criteria for the second-order nonlinear impulsive dynamic equation of the form
〖(r(t)g(x^∆ (t)))〗^∆+f(t,x^σ (t))=G(t,x^σ (t)),t≠θ_k ,k=1,2,…
x(t_k^+ )=ε_k (x(t_k^- )),x(t_k^+ )=h_k (x(t_k^- )),k=1,2,…
x(t_0^+ )=x_0,x^∆ (t_0^+ )=x_0^∆
on a time scale 𝕋 are presented. Our results generalize and extend some pervious results [17, 18, 19, 27]. These results are published in:
Journal of Analysis and Number Theory, 5 (2017), 147-154. [2]
In Chapter 6, Some new oscillation criteria for the second-order nonlinear impulsive delay dynamic equation with perturbation
〖(r(t〖)ω(t)|x^∆ (t)|〗^(α-1) x^∆ (t))〗^∆+Q(t,x(τ(t)))=P(t,x(τ(t)),x^∆ (t)),t ≠θ_k ,k=1,2,…
∆(r(t〖)ω(t)|x^∆ (t)|〗^(α-1) x^∆ (t))_(t=θ_k )+Q_k (θ_k,x(τ(θ_k)))=0,
on a time scale 𝕋 are established. Our results generalize and extend some pervious results [33, 37] and can be applied to some oscillation problems that not discussed before. These results extend the known results for the dynamic equations with and without impulses.
The results of this chapter are submitted for publication.