Delay differential equations

Keywords : Delay Differential Equations In the first chapter of this thesis which is composed of four chapters, the definition of the delay differential equation (DDE) is given. Furthermore, in this chapter functional differential equations are classified and examplified by describing in detail. Also, in the first chapter linear delay differential equations(LDDE) and the linear delay differential equation systems' (LDDES) definitions and in the theorem 1.7.1. converting each LDDE with n degree to a LDDES which is composed of n equation and n unknown function with the first degree is examined. Hence, all the results which are reached for the first degree LDDE can be expanded for the n degree LDDE is displayed. In the second chapter, first; the theorems are given for constant coefficient neutral delay differential equations' oscillations of solutions with this equation; x'(t) + px'(t-T) + qx(t-<7) = 0 t>t0 (NDDE) The most important part of all these is theorem 2.1.6 which includes if and only if conditions, for the oscillations of solutions. Then two NDDE with variable coefficient are taken and the conditions for their oscillations of solutions are examined. In the third chapter the differences between ordinary differential equations (ODE) and DDE are given. Even the rules of DDE are reached from the knowns for ODE, ODE are the special state of DDE which is accepted that the delay is zero. Moreover the continuity and the differences in the unique solution between ODE and DDE are expressed. And in the fourth chapter some solution methods for DDE are given. To x'(t) = ax(t - r) equation the solution is searched with step method and for x'(t) = f(t,x(t),x(t-T)) 0Keyword: Gecikmeli diferensiyel denklemler = Delay differential equations