Ebook: Infinite Interval Problems for Differential, Difference and Integral Equations

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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This monograph is a cumulation mainly of the author's 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 the illustration of almost all results with examples. This book should turn out to be a stimulus to the further development of the theory.
Audience: This work will be of interest to mathematicians and graduate students in the disciplines of theoretical and applied mathematics.

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This monograph is a cumulation mainly of the author's 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 the illustration of almost all results with examples. This book should turn out to be a stimulus to the further development of the theory.
Audience: This work will be of interest to mathematicians and graduate students in the disciplines of theoretical and applied mathematics.
Content:
Front Matter....Pages i-x
Second Order Boundary Value Problems....Pages 1-89
Higher Order Boundary Value Problems....Pages 90-109
Continuous Systems....Pages 110-138
Integral Equations....Pages 139-232
Discrete Systems....Pages 233-276
Equations in Banach Spaces....Pages 277-293
Multivalued Equations....Pages 294-328
Equations on Time Scales....Pages 329-338
Back Matter....Pages 339-341

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This monograph is a cumulation mainly of the author's 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 the illustration of almost all results with examples. This book should turn out to be a stimulus to the further development of the theory.
Audience: This work will be of interest to mathematicians and graduate students in the disciplines of theoretical and applied mathematics.
Content:
Front Matter....Pages i-x
Second Order Boundary Value Problems....Pages 1-89
Higher Order Boundary Value Problems....Pages 90-109
Continuous Systems....Pages 110-138
Integral Equations....Pages 139-232
Discrete Systems....Pages 233-276
Equations in Banach Spaces....Pages 277-293
Multivalued Equations....Pages 294-328
Equations on Time Scales....Pages 329-338
Back Matter....Pages 339-341
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