Oscillation behavior of solutions of second order functional differential equations

In this thesis, firstly, the path in the historical process of the second order functional differential equations (FDEs) and the studies on the oscillation behaviors of their solutions are explained. In the second chapter, giving the information about the definitions, the classifications and the applications of the FDEs and the oscillation of their solutions, the differences between the oscillatory behavior of the solutions of FDEs and ordinary differential equations (ODEs) are highlighted. At the end of the chapter, some examples about the studies on the oscillation behavior of the solutions of different types second-order FDE classes in the literature are given. After the third section, which includes the material and methodological information used in the thesis, the fourth chapter titled findings and discussion follows. In this chapter, the sufficient conditions about the oscillation of the solutions of the three different FDE classes , namely, second order linear neutral, half-linear neutral and linear mixed neutral with damping terms presented, respectively. The importance and applicability of the results obtained are shown with the examples given at the end of each subsection. In the fifth chapter what kind of generalizations can be achieved through the findings obtained and the methods used in this work has been mentioned. Also based on this thesis, some recommendations regarding the FDE classes in the forthcoming studies have been made. The thesis has been completed with the last chapter titled as references.