ABSTRACT
In this chapter, the authors deal with linear second order differential equations and always assume that they are expressed in Sturm-Liouville form The existence, uniqueness, and continuous dependence results that follow are established in a more general setting than is usual because no smoothness beyond continuity is assumed on the coefficient. In the examples that follow and are revisited throughout the chapter, the authors point out some important properties of Green's functions and typical behavior shared by many Sturm-Liouville eigenvalue problems that come up in applications. The reader may find it useful to revisit the four examples and the observations made about them while reading the rest of the chapter. The authors give a systematic development of Green's functions and their properties for regular Sturm-Liouville problems. A natural way to construct the Green's function in the case of mixed boundary data is through the variation of parameters formula for solving inhomogeneous initial value problems.
