Skip to main content

Counting compatible boundary conditions

  • Conference paper
  • First Online:
Global Theory of Dynamical Systems

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 819))

  • 1093 Accesses

Abstract

The index theorem of M. Morse, which counts focal points weighted by multiplicity in positive regular problems, and the extension by the author, which counts focal points weighted by a signature in problems not required to be positive regular, are further extended to the counting of compatible sets of general self-adjoint boundary conditions. Circumstances under which the weight is the multiplicity are exhibited.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bliss, G. A., Lectures on the Calculus of Variations, University of Chicago Press, 1946.

    Google Scholar 

  2. Morse, M., The calculus of variations in the large, Am. Math. Soc. Coll. Publ. XVIII, 1934.

    Google Scholar 

  3. Pitcher, E., The variation in index of a quadratic function depending on a parameter, Bull. Am. Math. Soc., 65 (1959), 355–357.

    Article  MathSciNet  MATH  Google Scholar 

  4. Pitcher, E., Conjugate points without the condition of Legendre, Optimal Control and Differential Equations, A. B. Schwarzkopf, Walter G. Kelley, and Stanley B. Eliason, Editors, 223–244, Academic Press, 1978.

    Google Scholar 

  5. Pitcher, E., Counting focal points and characteristic roots, Bull. Inst. of Math. Acad. Sin., 6 (1978), 389–413.

    MathSciNet  MATH  Google Scholar 

  6. Reid, W.T., Ordinary differential equations, Wiley, 1971.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Zbigniew Nitecki Clark Robinson

Rights and permissions

Reprints and permissions

Copyright information

© 1980 Springer-Verlag

About this paper

Cite this paper

Pitcher, E. (1980). Counting compatible boundary conditions. In: Nitecki, Z., Robinson, C. (eds) Global Theory of Dynamical Systems. Lecture Notes in Mathematics, vol 819. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087001

Download citation

  • DOI: https://doi.org/10.1007/BFb0087001

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10236-6

  • Online ISBN: 978-3-540-38312-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics