The theory of differential equations. Classical and qualitative
type: Item
instance of: scholarly article
title: The theory of differential equations. Classical and qualitative
zbMATH Open document ID: 1201.34001
DOI: 10.1007/978-1-4419-5783-2
author: Walter G. Kelley
author: Allan Peterson
published in: Universitext
publication date: 2010-04-26T00:00:00Z
review text: 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.
reviewed by: Ludvík Janoš
Mathematics Subject Classification ID: 34-01
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 5701452
describes a project that uses: Mathematica
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-1-4419-5783-2
OpenAlex ID: W2493294075
description: scientific article; zbMATH DE number 5701452