Hardcover ISBN:  9780821846940 
Product Code:  GSM/129 
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eBook ISBN:  9780821884850 
Product Code:  GSM/129.E 
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AMS Member Price:  $68.00 
Hardcover ISBN:  9780821846940 
eBook: ISBN:  9780821884850 
Product Code:  GSM/129.B 
List Price:  $184.00 $141.50 
MAA Member Price:  $165.60 $127.35 
AMS Member Price:  $147.20 $113.20 
Hardcover ISBN:  9780821846940 
Product Code:  GSM/129 
List Price:  $99.00 
MAA Member Price:  $89.10 
AMS Member Price:  $79.20 
eBook ISBN:  9780821884850 
Product Code:  GSM/129.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9780821846940 
eBook ISBN:  9780821884850 
Product Code:  GSM/129.B 
List Price:  $184.00 $141.50 
MAA Member Price:  $165.60 $127.35 
AMS Member Price:  $147.20 $113.20 

Book DetailsGraduate Studies in MathematicsVolume: 129; 2012; 373 ppMSC: Primary 34; 35; 37;
This text emphasizes rigorous mathematical techniques for the analysis of boundary value problems for ODEs arising in applications. The emphasis is on proving existence of solutions, but there is also a substantial chapter on uniqueness and multiplicity questions and several chapters which deal with the asymptotic behavior of solutions with respect to either the independent variable or some parameter. These equations may give special solutions of important PDEs, such as steady state or traveling wave solutions. Often two, or even three, approaches to the same problem are described. The advantages and disadvantages of different methods are discussed.
The book gives complete classical proofs, while also emphasizing the importance of modern methods, especially when extensions to infinite dimensional settings are needed. There are some new results as well as new and improved proofs of known theorems. The final chapter presents three unsolved problems which have received much attention over the years.
Both graduate students and more experienced researchers will be interested in the power of classical methods for problems which have also been studied with more abstract techniques. The presentation should be more accessible to mathematically inclined researchers from other areas of science and engineering than most graduate texts in mathematics.
ReadershipGraduate students and research mathematicians interested in ODEs and PDEs.

Table of Contents

Chapters

Chapter 1. Introduction

Chapter 2. An introduction to shooting methods

Chapter 3. Some boundary value problems for the Painlevé transcendents

Chapter 4. Periodic solutions of a higher order system

Chapter 5. A linear example

Chapter 6. Homoclinic orbits of the FitzHughNagumo equations

Chapter 7. Singular perturbation problems—rigorous matching

Chapter 8. Asymptotics beyond all orders

Chapter 9. Some solutions of the FalknerSkan equation

Chapter 10. Poiseuille flow: Perturbation and decay

Chapter 11. Bending of a tapered rod; variational methods and shooting

Chapter 12. Uniqueness and multiplicity

Chapter 13. Shooting with more parameters

Chapter 14. Some problems of A. C. Lazer

Chapter 15. Chaotic motion of a pendulum

Chapter 16. Layers and spikes in reactiondiffusion equations, I

Chapter 17. Uniform expansions for a class of second order problems

Chapter 18. Layers and spikes in reactiondiffusion equations, II

Chapter 19. Three unsolved problems


Additional Material

Reviews

This book brings a new and innovative look to several areas of the theory of ordinary differential equations. It is certainly a very refreshing addition to the existing literature. Students of mathematics who have avoided (for various reasons) differential equations need this volume as an antidote. ...a most informative, stimulating, and refreshing book!
MAA Reviews 
This wellconceived and wellpresented monograph uniquely provides us an opportunity to learn how these experts analyze a wide variety of boundary value problems of current interest and how they interpret and utilize the relevant recent literature. The skills they display are potent, and they're not found in other textbooks.
Robert E. O'Malley, SIAM Book Reviews


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This text emphasizes rigorous mathematical techniques for the analysis of boundary value problems for ODEs arising in applications. The emphasis is on proving existence of solutions, but there is also a substantial chapter on uniqueness and multiplicity questions and several chapters which deal with the asymptotic behavior of solutions with respect to either the independent variable or some parameter. These equations may give special solutions of important PDEs, such as steady state or traveling wave solutions. Often two, or even three, approaches to the same problem are described. The advantages and disadvantages of different methods are discussed.
The book gives complete classical proofs, while also emphasizing the importance of modern methods, especially when extensions to infinite dimensional settings are needed. There are some new results as well as new and improved proofs of known theorems. The final chapter presents three unsolved problems which have received much attention over the years.
Both graduate students and more experienced researchers will be interested in the power of classical methods for problems which have also been studied with more abstract techniques. The presentation should be more accessible to mathematically inclined researchers from other areas of science and engineering than most graduate texts in mathematics.
Graduate students and research mathematicians interested in ODEs and PDEs.

Chapters

Chapter 1. Introduction

Chapter 2. An introduction to shooting methods

Chapter 3. Some boundary value problems for the Painlevé transcendents

Chapter 4. Periodic solutions of a higher order system

Chapter 5. A linear example

Chapter 6. Homoclinic orbits of the FitzHughNagumo equations

Chapter 7. Singular perturbation problems—rigorous matching

Chapter 8. Asymptotics beyond all orders

Chapter 9. Some solutions of the FalknerSkan equation

Chapter 10. Poiseuille flow: Perturbation and decay

Chapter 11. Bending of a tapered rod; variational methods and shooting

Chapter 12. Uniqueness and multiplicity

Chapter 13. Shooting with more parameters

Chapter 14. Some problems of A. C. Lazer

Chapter 15. Chaotic motion of a pendulum

Chapter 16. Layers and spikes in reactiondiffusion equations, I

Chapter 17. Uniform expansions for a class of second order problems

Chapter 18. Layers and spikes in reactiondiffusion equations, II

Chapter 19. Three unsolved problems

This book brings a new and innovative look to several areas of the theory of ordinary differential equations. It is certainly a very refreshing addition to the existing literature. Students of mathematics who have avoided (for various reasons) differential equations need this volume as an antidote. ...a most informative, stimulating, and refreshing book!
MAA Reviews 
This wellconceived and wellpresented monograph uniquely provides us an opportunity to learn how these experts analyze a wide variety of boundary value problems of current interest and how they interpret and utilize the relevant recent literature. The skills they display are potent, and they're not found in other textbooks.
Robert E. O'Malley, SIAM Book Reviews