Celik, Derya
M.S., Mathematics
Supervisor : Accoc.Prof.Dr.Agacik Zafer
Co-supervisor : Prof.Dr.Marat Akhmet
June 2002, 39 pages

In this thesis, integral manifolds of quasilinear impulsive systems are investigated. The thesis consists of two chapters. Chapter 1 is introductory in nature. Its main purpose is to provide some basic definitions and theorems that are useful in obtaining the main results. Namely, we give Gronwall-Bellman type lemmas, a continuous dependence result, a box diagonalization method, Banach fixed point theorem and a general theorem about integral manifolds. In chapter 2, we state and prove two new theorems. A theorem on the existence of an integral manifold and a theorem on the periodicity of the integral manifold are obtained.

Keywords : Impulsive differential system,Gronwall-Bellman inequality,hyperbolic system,quasilinear system,successive approximation,Lyapunov function,integral

Celik, Derya
Yüksek.Lisans., Matematik
Supervisor : Accoc.Prof.Dr.Agacik Zafer
Co-supervisor : Prof.Dr.Marat Akhmet
Haziran 2002, 39 sayfa

Bu tezde yari lineer "impulsive" sistemlerin integral manifoldlari incelenmistir. Tez iki bolumden olusmaktadir. Ilk bolumde daha sonra kullanacagimiz bazi temel tanim ve teoremler verilmistir. Gronwall-Bellman tipi on teoremler, integral manifold uzerine bir genel teorem, bir kosegenlestirme metodu ve Banach sabit nokta teoremi bunlardan bazilaridir. Ikinci bolumde integral manifoldun varligi ve periyodikligi ile ilgili iki yeni teorem kanitlariyla beraber verilmistir.

Anahtar Kelimeler : "Impulsive" diferansiyel sistem,Gronwall-Bellman esitsizligi,hiperbolik sistem,yari lineer sistem,ardisik yaklasimlar,Lyapunov fonksiyonu,integral manifold, periyodiklik.