| Title:
|
Quadratic functionals with a variable singular end point (English) |
| Author:
|
Došlá, Zuzana |
| Author:
|
Zezza, PierLuigi |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
33 |
| Issue:
|
3 |
| Year:
|
1992 |
| Pages:
|
411-425 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we introduce the definition of coupled point with respect to a (scalar) quadratic functional on a noncompact interval. In terms of coupled points we prove necessary (and sufficient) conditions for the nonnegativity of these functionals. (English) |
| Keyword:
|
quadratic functional |
| Keyword:
|
singular quadratic functional |
| Keyword:
|
Euler-Lagrange equation |
| Keyword:
|
conjugate point |
| Keyword:
|
coupled point |
| Keyword:
|
singularity condition |
| MSC:
|
34A10 |
| MSC:
|
34A12 |
| MSC:
|
34C10 |
| MSC:
|
49B10 |
| MSC:
|
49K05 |
| MSC:
|
49K15 |
| idZBL:
|
Zbl 0779.49026 |
| idMR:
|
MR1209284 |
| . |
| Date available:
|
2009-01-08T17:56:55Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118510 |
| . |
| Reference:
|
[1] Morse M., Leighton W.: Singular quadratic functionals.Trans. Amer. Math. Soc. 40 (1936), 252-286. Zbl 0015.02701, MR 1501873 |
| Reference:
|
[2] Leighton W.: Principal quadratic functionals.Trans. Amer. Math. Soc. 67 (1949), 253-274. Zbl 0041.22404, MR 0034535 |
| Reference:
|
[3] Leighton W., Martin A.D.: Quadratic functionals with a singular end point.Trans. Amer. Math. Soc. 78 (1955), 98-128. Zbl 0064.35401, MR 0066570 |
| Reference:
|
[4] Reid W.T.: Sturmian theory for ordinary differential equations.Springer-Verlag 1980. Zbl 0459.34001, MR 0606199 |
| Reference:
|
[5] Zeidan V., Zezza P.: Coupled points in the calculus of variations and applications to periodic problems.Trans. Amer. Math. Soc. 315 (1989), 323-335. Zbl 0677.49020, MR 0961599 |
| Reference:
|
[6] Zeidan V., Zezza P.: Variable end points in the calculus of variations: Coupled points.in ``Analysis and Optimization of Systems'', A. Bensoussan, J.L. Lions eds., Lectures Notes in Control and Information Sci. 111, Springer-Verlag, Heidelberg, 1988. MR 0956284 |
| Reference:
|
[7] Zezza P.: The Jacobi condition for elliptic forms in Hilbert spaces.JOTA 76 (1993). MR 1203907 |
| Reference:
|
[8] Zezza P., Došlá Z.: Coupled points in the calculus of variations and optimal control theory via the quadratic form theory.preprint. |
| Reference:
|
[9] Coppel W.A.: Disconjugacy.Lecture Notes in Math. 220, Springer-Verlag, Berlin-Heidelberg, 1971. Zbl 0224.34003, MR 0460785 |
| . |
