Abstract
This chapter presents existence theory for second order boundary value problems on infinite intervals. There are two major approaches in the literature to establish existence of solutions to boundary value problems on infinite intervals. The first approach is based on a diagonalization process whereas the second is based on the Furi-Pera fixed point theorem. Both approaches will be presented in this chapter. In Section 1.2 we list several examples from the real world phenomena which motivate the study of boundary value problems on infinite intervals. In Section 1.3 we discuss some infinite interval problems which date back to 1896 and state several fundamental results which are well known.
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