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Applied Mathematical Sciences

Nonlinear Singular Perturbation Phenomena

Theory and Applications

Authors: Chang, K. W., Howes, F. A.

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About this book

Our purpose in writing this monograph is twofold. On the one hand, we want to collect in one place many of the recent results on the exist­ ence and asymptotic behavior of solutions of certain classes of singularly perturbed nonlinear boundary value problems. On the other, we hope to raise along the way a number of questions for further study, mostly ques­ tions we ourselves are unable to answer. The presentation involves a study of both scalar and vector boundary value problems for ordinary dif­ ferential equations, by means of the consistent use of differential in­ equality techniques. Our results for scalar boundary value problems obeying some type of maximum principle are fairly complete; however, we have been unable to treat, under any circumstances, problems involving "resonant" behavior. The linear theory for such problems is incredibly complicated already, and at the present time there appears to be little hope for any kind of general nonlinear theory. Our results for vector boundary value problems, even those admitting higher dimensional maximum principles in the form of invariant regions, are also far from complete. We offer them with some trepidation, in the hope that they may stimulate further work in this challenging and important area of differential equa­ tions. The research summarized here has been made possible by the support over the years of the National Science Foundation and the National Science and Engineering Research Council.

Table of contents (8 chapters)

  • Introduction

    Chang, K. W. (et al.)

    Pages 1-5

  • A’priori Bounds and Existence Theorems

    Chang, K. W. (et al.)

    Pages 6-17

  • Semilinear Singular Perturbation Problems

    Chang, K. W. (et al.)

    Pages 18-36

  • Quasilinear Singular Perturbation Problems

    Chang, K. W. (et al.)

    Pages 37-60

  • Quadratic Singular Perturbation Problems

    Chang, K. W. (et al.)

    Pages 61-90

Buy this book

eBook $89.00
price for USA in USD (gross)
  • ISBN 978-1-4612-1114-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $119.00
price for USA in USD
  • ISBN 978-0-387-96066-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Nonlinear Singular Perturbation Phenomena
Book Subtitle
Theory and Applications
Authors
Series Title
Applied Mathematical Sciences
Series Volume
56
Copyright
1984
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-1114-3
DOI
10.1007/978-1-4612-1114-3
Softcover ISBN
978-0-387-96066-1
Series ISSN
0066-5452
Edition Number
1
Number of Pages
VIII, 180
Number of Illustrations
1 b/w illustrations
Topics