Appendix

Abstract

In this chapter we provide basic facts of the theory of operators of monotone type, as well as the calculus of Clarke’s generalized gradient as it is used in Chaps. 3, 4, and 5. The focus, however, is on the basic analysis of vectorvalued, HL integrable functions used in the theory of differential and integral equations and inclusions presented in Chaps. 6–7, which represents in itself a new development that is of interest in its own. With the tools provided by that theory we are able to convert the problems under consideration into operator equations and inclusions that then can be solved by means of the results derived in Chap. 2, see Chaps. 6–7. The application of the order-theoretic results of Chap. 2 to the problems studied in Chaps. 6–7 requires a detailed analysis about the existence of supremums and infimums of chains, as well as the existence of order centers of sets in ordered function spaces, which is provided in Sect. 9.2.