The theory of differential equations. Classical and qualitative
This book provides an introduction to many of the important topics associated with ordinary differential equations. It consists of eight chapters. Chapters 1 and 2 treat the first-order linear equations and introduce the reader to the theory of periodicity of solutions, i.e., the Floquet theory. Chapter 3 is on autonomous systems, studying differential equations via the dynamical systems theory. Chapter 4 is on perturbation theory and chapters 5 and 6 return to linear equations and present a rich mix of classical subjects, such as self-adjointness, disconjugacy, Green functions, Riccati equations and the calculus of variations. Chapter 7 deals with boundary value problems, and introduces the contraction mapping theorem as a tool in proving existence and uniqueness of solutions. The last chapter has a theoretical character. It concerns Lipschitz conditions, the Picard-Lindelöf theorem, Ascoli-Arzela theorem, and extendability of solutions.
scientific article; zbMATH DE number 5701452