Advertisement

Nonlinear Singular Perturbation Phenomena

Theory and Applications

  • K. W. Chang
  • F. A. Howes

Part of the Applied Mathematical Sciences book series (AMS, volume 56)

Table of contents

  1. Front Matter
    Pages N2-viii
  2. K. W. Chang, F. A. Howes
    Pages 1-5
  3. K. W. Chang, F. A. Howes
    Pages 6-17
  4. K. W. Chang, F. A. Howes
    Pages 18-36
  5. K. W. Chang, F. A. Howes
    Pages 37-60
  6. K. W. Chang, F. A. Howes
    Pages 61-90
  7. K. W. Chang, F. A. Howes
    Pages 91-105
  8. K. W. Chang, F. A. Howes
    Pages 106-122
  9. K. W. Chang, F. A. Howes
    Pages 123-170
  10. Back Matter
    Pages 171-181

About this book

Introduction

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.

Keywords

Area Boundary value problem DEX Invariant behavior boundary element method eXist equation form maximum online perturbation theory presentation techniques time

Authors and affiliations

  • K. W. Chang
    • 1
  • F. A. Howes
    • 2
  1. 1.Department of MathematicsUniversity of CalgaryCalgaryCanada
  2. 2.Department of MathematicsUniversity of CaliforniaDavisUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1114-3
  • Copyright Information Springer-Verlag New York, Inc. 1984
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-96066-1
  • Online ISBN 978-1-4612-1114-3
  • Series Print ISSN 0066-5452
  • Buy this book on publisher's site