Oscillatory behaviour of solutions of impulsive delay equations

This thesis consists of four chapters. The first chapter is devoted to the int- roduction and provides a generel knowledge about the existing literature. In the second chapter, we give some basic definitions and preliminary results that will be used in further sections. In the third chapter, we offer a oscillatory condition for the second order impulsive delay linear differential equation given by(a(t)x?(t))?+p(t)x(t-?)=0,t?t? , t?t_{k}x(t_{k}?)=b_{k}x(t_{k}) , x?(t_{k}?)=c_{k}x?(t_{k})k=1,2,...is given. In the fourth chapter, we investigate the oscillatory behaviour of the solutions of the following impulsive delay difference equations with continuous arguments:?_{?}x(t)+?p_{i}(t)x(t-?_{i})=0, t?[t?,?)\{?_{n}}_{n?N}?x(?_{n})+q_{n}x(?_{n})=0, n?Nby making comparison with appropriate nonimpulsive delay difference and differential equations. Also, the oscillatory behaviour of solutions of the mixed type impulsive delay difference equation with continuous arguments?_{?}x(t)+p(t)x(t-?)+q(t)x(t+?)=0, t?[t?,?)\{?_{k}}_{k?N}?x(?_{k})+q_{k}x(?_{k})=0, k?Nis studied.