Applications to Infinite Systems of Differential Equations

Abstract

In this chapter we apply the machinery developed previously to the theory of ordinary differential equations in Banach spaces. In particular, we show that several infinite systems of differential equations in some Banach sequence spaces can be treated from the view point of the theory of differential equations in Banach spaces. Moreover, using some specific features of sequence spaces we are able to formulate several results concerning the solvability of infinite systems of differential equations in numerous sequence spaces and to characterize solutions of those systems. We illustrate results presented in this chapter by many concrete examples.