Hostname: page-component-5c6d5d7d68-tdptf Total loading time: 0 Render date: 2024-08-29T13:28:43.622Z Has data issue: false hasContentIssue false
  • English
  • Français

The Expansion Problem with Boundary Conditions at a Finite Set of Points

Published online by Cambridge University Press:  20 November 2018

Randal H. Cole
Randal H. Cole*
Affiliation:
University of Western Ontario
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The problem of expanding an arbitrary function in a series of characteristic solutions of the ordinary differential equation

(1.1)

and the boundary relations

(1.2)

is well known. The various discussions are distinguished by the manner in which a parameter λ appears in the differential system and by the number of points at which the boundary conditions apply. The case in which the boundary conditions apply at intermediate as well as at the end points of a fundamental interval has been considered by Wilder (3).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 13 , 1961 , pp. 462 - 479
Copyright
Copyright © Canadian Mathematical Society 1961

References

1. Langer, R. E., The boundary problem of an ordinary linear differential system in the complex domain, Trans. Amer. Math. Soc, 46 (1939), 151–190.Google Scholar
2. Langer, R. E., Developments associated with a boundary problem not linear in the parameter, Trans. Amer. Math. Soc, 25 (1923), 155–172.Google Scholar
3. Wilder, C. E., Expansion problems of ordinary linear differential equations with auxiliary conditions at more than two points, Trans. Amer. Math. Soc, 18 (1917), 415–442.Google Scholar
4. Cole, R. H., Reduction of an n-th order differential equation and m-point boundary conditions to an equivalent matrix system, Amer. J. Math. (1), 68 (1946), 179–184.Google Scholar
5. Haltiner, G. H., The theory of linear differential systems based upon a new definition of the adjoint, Duke Math. J., 15 (1948), 893–919.Google Scholar
6. Whyburn, W. M., Differential systems with general boundary conditions, Seminar Reports in Mathematics, University of California Publ. Math. (1), 2 (1944), 45–61.Google Scholar
7. Whyburn, W. M., Differential equations with general boundary conditions, Bull. Amer. Math. Soc. (10), 48 (1942), 692–704.Google Scholar
8. Whyburn, W. M., Differential systems with boundary conditions at more than two points, Proceedings of the Conference on Differential Equations, held at the University of Maryland, March 17-19, 1955 (University of Maryland Bookstore, College Park, Md., 1956), 1–21.Google Scholar