| Title:
|
Singular quadratic functionals of one dependent variable (English) |
| Author:
|
Došlá, Zuzana |
| Author:
|
Došlý, Ondřej |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
36 |
| Issue:
|
2 |
| Year:
|
1995 |
| Pages:
|
219-237 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Singular quadratic functionals of one dependent variable with nonseparated boundary conditions are investigated. Necessary and sufficient conditions for nonnegativity of these functionals are derived using the concept of {\it coupled point} and {\it singularity condition}. The paper also includes two comparison theorems for coupled points with respect to the various boundary conditions. (English) |
| Keyword:
|
quadratic functional |
| Keyword:
|
singular quadratic functional |
| Keyword:
|
periodic and antiperiodic boundary condition |
| Keyword:
|
conjugate point |
| Keyword:
|
coupled point |
| Keyword:
|
singularity condition |
| MSC:
|
34A10 |
| MSC:
|
34C10 |
| MSC:
|
49B10 |
| MSC:
|
49K05 |
| MSC:
|
49N10 |
| idZBL:
|
Zbl 0838.34036 |
| idMR:
|
MR1357523 |
| . |
| Date available:
|
2009-01-08T18:17:25Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118750 |
| . |
| Reference:
|
[1] Coppel W.A.: Disconjugacy.Lectures Notes in Math. 220 Springer Verlag, 1971. Zbl 0224.34003, MR 0460785 |
| Reference:
|
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| Reference:
|
[3] Došlá Z., Zezza P.: Singular quadratic functionals with variable end point.Comment. Math. Univ. Carolinae 33 (1992), 411-425. MR 1209284 |
| Reference:
|
[4] Došlá Z., Zezza P.: Coupled points in the calculus of variations and optimal control theory via the quadratic form theory.Diff. Equations and Dynamical Systems 2 (1994), 137-152. MR 1386044 |
| Reference:
|
[5] Hestenes M.G.: Applications of the theory of quadratic forms in Hilbert space to the calculus of variations.Pacific J. Math 1 (1951), 525-581. Zbl 0045.20806, MR 0046590 |
| Reference:
|
[6] Leighton W., Morse M.: Singular quadratic functionals.Trans. Amer. Math. Soc. 40 (1936), 252-286. Zbl 0015.02701, MR 1501873 |
| Reference:
|
[7] Leighton W.: Principal quadratic functionals.Trans. Amer. Math. Soc. 67 (1949), 253-274. Zbl 0041.22404, MR 0034535 |
| Reference:
|
[8] 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:
|
[9] Reid W.T.: Sturmian theory for ordinary differential equations.Springer Verlag, 1980. Zbl 0459.34001, MR 0606199 |
| Reference:
|
[10] Stein J.: Hilbert space and variational methods for singular selfadjoint systems of differential equations.Bull. Amer. Math. Soc. 80 (1974), 744-747. Zbl 0289.34039, MR 0417486 |
| Reference:
|
[11] Tomastik E.C.: Singular quadratic functionals of $n$ dependent variables.Trans. Amer. Math. Soc. 124 (1966), 60-76. Zbl 0161.09503, MR 0196556 |
| Reference:
|
[12] Tomastik E.C.: Principal quadratic functionals.Trans. Amer. Math. Soc. 218 (1976), 297-309. Zbl 0346.49013, MR 0405208 |
| Reference:
|
[13] 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:
|
[14] 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:
|
[15] Zezza P.: The Jacobi condition for elliptic forms in Hilbert spaces,.JOTA 76 (1993), 357-380. MR 1203907 |
| . |
