ABSTRACT
This chapter discusses certain boundary value problems (BVPs) associated with second order functional differential equations (FDEs). Although the study of the existence and location of zeros of the solutions of ordinary differential equations is fundamental in the study of BVPs for such equations, the relation between solutions to certain BVPs for FDEs and the oscillatory behavior of such solutions is less clear. The chapter presents a number of approaches to the study of such problems, which, in some sense, parallels the corresponding techniques for BVPs associated with ODEs. It argues that these techniques will give an idea of what may be obtained. The chapter establishes existence via Lipschitz and Nagumo-type methods, respectively. It employs topological methods, and deals with existence and uniqueness for a certain type of singular problem. The chapter also presents the definition of the norm by introducing a weight function.
