ABSTRACT
This chapter introduces some basic concepts from the theory of functional differential equations and discusses the problems in oscillation theory and boundary value problems of functional differential equations. It is concerned with the statement of the basic initial value problems and classification of equations with deviating arguments. The chapter shows the main problems in the oscillation theory of differential equations with deviating arguments. It explains the formulation of the boundary value problem of functional differential equations. The chapter presents some fixed point theorems which are important tools while studying the existence of solutions for initial value problems and boundary value problems. The main sources of boundary value problems for ordinary differential equations without deviating arguments are boundary value problems for partial differential equations. For functional differential equations the situation is different. The usual sources of boundary value problems for functional differential equations arise from variational problems for these equations.
