Asymptotic behaviour of solutions of dynamic equations on time scales

In this thesis, asymptotic behaviour of solutions of dynamic equations on unbounded time scales is studied.The thesis consists of five chapters.The first chapter is devoted to introduction.In the second chapter, necessary information concerning the time scale concept is given.In the third and fourth chapters, we study both bounded and unbounded solutions of equations of the form$$\big[x(t)+A(t)x(\alpha(t))\big]^{\Delta}+B(t)x(\beta(t))-C(t)x(\gamma(t))=\varphi(t),\quad t\in[t_{0},\infty)_{\mathbb{T}}$$and$$\big[x(t)+A(t)x(\alpha(t))\big]^{\Delta^{2}}+B(t)x(\beta(t))-C(t)x(\gamma(t))=\varphi(t),\quad t\in[t_{0},\infty)_{\mathbb{T}},$$respectively.In the last chapter, we first study bounded solutions of equations of the form$$\big[x(t)+A(t)x(\alpha(t))\big]^{\Delta^{n}}+B(t)x(\beta(t))-C(t)x(\gamma(t))=\varphi(t),\quad t\in[t_{0},\infty)_{\mathbb{T}},$$and then we confine our attention to unbounded solutions of equations of the form$$\big[x(t)+A(t)x(\alpha(t))\big]^{\Delta^{n}}+B(t)x(\beta(t))=\varphi(t),\quad t\in[t_{0},\infty)_{\mathbb{T}}.$$