Infinite Interval Problems for Differential, Difference and Integral Equations

1. Front Matter

   Pages i-x

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2. Second Order Boundary Value Problems

   • Ravi P. Agarwal, Donal O’Regan

   Pages 1-89

3. Higher Order Boundary Value Problems

   • Ravi P. Agarwal, Donal O’Regan

   Pages 90-109

4. Continuous Systems

   • Ravi P. Agarwal, Donal O’Regan

   Pages 110-138

5. Integral Equations

   • Ravi P. Agarwal, Donal O’Regan

   Pages 139-232

6. Discrete Systems

   • Ravi P. Agarwal, Donal O’Regan

   Pages 233-276

7. Equations in Banach Spaces

   • Ravi P. Agarwal, Donal O’Regan

   Pages 277-293

8. Multivalued Equations

   • Ravi P. Agarwal, Donal O’Regan

   Pages 294-328

9. Equations on Time Scales

   • Ravi P. Agarwal, Donal O’Regan

   Pages 329-338

10. Back Matter

    Pages 339-341

    PDF

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.

• Boundary value problem
• DEX
• Finite
• Integral equation
• banach spaces
• development
• eXist
• equation
• integral
• mathematics
• time
• ordinary differential equations

'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)

• National University of Singapore, Singapore, Republic of Singapore

  Ravi P. Agarwal

• University of Ireland, Galway, Ireland

  Donal O’Regan

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