Infinite Interval Problems for Differential, Difference and Integral Equations - Softcover

Agarwal, R.P. P.; O'Regan, Donal

 
9789401038348: Infinite Interval Problems for Differential, Difference and Integral Equations
Softcover
ISBN 10: 9401038341 ISBN 13: 9789401038348
Verlag: Springer, 2012

Inhaltsangabe

Infinite interval problems abound in nature and yet until now there has been no book dealing with such problems. The main reason for this seems to be that until the 1970’s for the infinite interval problem all the theoretical results available required rather technical hypotheses and were applicable only to narrowly defined classes of problems. Thus scientists mainly offer~d and used special devices to construct the numerical solution assuming tacitly the existence of a solution. In recent years a mixture of classical analysis and modern fixed point theory has been employed to study the existence of solutions to infinite interval problems. This has resulted in widely applicable results. This monograph is a cumulation mainly of the authors’ research over a period of more than ten years and offers easily verifiable existence criteria for differential, difference and integral equations over the infinite interval. An important feature of this monograph is that we illustrate almost all the results with examples. The plan of this monograph is as follows. In Chapter 1 we present the existence theory for second order boundary value problems on infinite intervals. We begin with several examples which model real world phenom­ ena. A brief history of the infinite interval problem is also included. We then present general existence results for several different types of boundary value problems. Here we note that for the infinite interval problem only two major approaches are available in the literature.

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Críticas

'the monograph is well written and will be of interest for mathematicians and graduate students with research interest in applied mathematics.'
Zentral Blatt Mathematik, 988 (2002)

Reseña del editor

Infinite interval problems abound in nature and yet until now there has been no book dealing with such problems. The main reason for this seems to be that until the 1970's for the infinite interval problem all the theoretical results available required rather technical hypotheses and were applicable only to narrowly defined classes of problems. Thus scientists mainly offer~d and used special devices to construct the numerical solution assuming tacitly the existence of a solution. In recent years a mixture of classical analysis and modern fixed point theory has been employed to study the existence of solutions to infinite interval problems. This has resulted in widely applicable results. This monograph is a cumulation mainly of the authors' research over a period of more than ten years and offers easily verifiable existence criteria for differential, difference and integral equations over the infinite interval. An important feature of this monograph is that we illustrate almost all the results with examples. The plan of this monograph is as follows. In Chapter 1 we present the existence theory for second order boundary value problems on infinite intervals. We begin with several examples which model real world phenom­ ena. A brief history of the infinite interval problem is also included. We then present general existence results for several different types of boundary value problems. Here we note that for the infinite interval problem only two major approaches are available in the literature.

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Verlag
Springer
Erscheinungsdatum
2012
Sprache
Englisch
ISBN 10 
9401038341
ISBN 13 
9789401038348
Einband
Tapa blanda
Anzahl der Seiten
356
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
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Vorgestellte Ausgabe

ISBN 10:  0792369610 ISBN 13:  9780792369615
Verlag: Springer, 2001
Hardcover