Existence Theory for Nonlinear Ordinary Differential Equations - Couverture rigide

O'Regan, Donal

Couverture rigide

ISBN 10 : 0792345118 ISBN 13 : 9780792345114

Editeur : Kluwer Academic Publishers, 1997

Synopsis

We begin our applications of fixed point methods with existence of solutions to certain first order initial initial value problems. This problem is relatively easy to treat, illustrates important methods, and in the end will carry us a good deal further than may first meet the eye. Thus, we seek solutions to Y'. = I(t, y) (1. 1 ) { yeO) = r n where I: I X R n ---+ R and I = [0, b]. We shall seek solutions that are de- fined either locally or globally on I, according to the assumptions imposed on I. Notice that (1. 1) is a system of first order equations because I takes its values in Rn. In section 3. 2 we will first establish some basic existence theorems which guarantee that a solution to (1. 1) exists for t > 0 and near zero. Familiar examples show that the interval of existence can be arbi- trarily short, depending on the initial value r and the nonlinear behaviour of I. As a result we will also examine in section 3. 2 the dependence of the interval of existence on I and r. We mention in passing that, in the results which follow, the interval I can be replaced by any bounded interval and the initial value can be specified at any point in I. The reasoning needed to cover this slightly more general situation requires minor modifications on the arguments given here.

A propos du livre

Présentation de l'éditeur

This book presents an up-to-date account of many topics of current interest in the theory of nonlinear ordinary differential equations. Topics include fixed point theory, periodic problems, lower and upper surfaces, positone and semi-positone problems, singular equations, limit circle problems, finite and infinite interval problems, and impulsive differential equations. In addition many important applications are presented to complement the theory. Audience: This work will be of interest to theoretical and applied mathematicians, and graduate students in the above disciplines.

Détails de l'édition

• Éditeur: Kluwer Academic Publishers
• Date d'édition: 1997
• Langue: anglais
• ISBN 10: 0792345118
• ISBN 13: 9780792345114
• Reliure: Relié
• Nombre de pages: 207
• Coordonnées du fabricant: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Allemagne