Oscillation of first order nonlinear delay differential equations

This thesis consists of five chapters. The first chapter is devoted to the introduction section and provide a generel knowledge of literature. In the second chapter, we mention some basic notions and studies so far. Third and fourth chapters are devoted to our original results. In the third chapter, new oscillation conditions for the solutions of first order nonlinear delay differential equation given by u^' (t)+p(t)f(u(σ(t)))=0 are obtained. Also, new oscillation conditions for the solutions of first order nonlinear delay differential equation with several nonmonotone arguments given by u^' (t)+∑_(i=1)^m▒〖p_i (t) f_i (u(σ_i (t)))=0〗 are offered. In the fourth chapter, new oscillation criteria for the solutions of first order nonlinear advanced differential equation given by u^' (t)-p(t)f(u(σ(t)))=0 are obtained. Then, new oscillation criteria for the solutions of first order nonlinear advanced differential equation with several nonmonotone arguments given by u^' (t)-∑_(i=1)^m▒〖p_i (t) f_i (u(σ_i (t)))=0〗 are presented. In the fifth chapter, discussions and conclusions are given. Keywords: Differential equation. Delay differential equation, Advanced differential equation, Monotone argument, Nonmonotone argument, Oscillatory solution, Nonoscillatory solution.