Theory of First Order Differential Equations

Abstract

Many questions in the theory of differential equations can be answered in a particularly elegant manner using general concepts of functional analysis. In this and later chapters, functional-analytic methods will be used to derive theorems on existence, uniqueness, and dependence of solutions on parameters. We begin by introducing the concept of a Banach space.KeywordsBanach SpaceGlobal SolutionFixed Point TheoremUniqueness TheoremLipschitz ConditionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.