Singular quadratic functionals of one dependent variable
Commentationes Mathematicae Universitatis Carolinae (1995)
- Volume: 36, Issue: 2, page 219-237
- ISSN: 0010-2628
Access Full Article
topAbstract
topHow to cite
topDošlá, Zuzana, and Došlý, Ondřej. "Singular quadratic functionals of one dependent variable." Commentationes Mathematicae Universitatis Carolinae 36.2 (1995): 219-237. <http://eudml.org/doc/247703>.
@article{Došlá1995,
abstract = {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 coupled point and singularity condition. The paper also includes two comparison theorems for coupled points with respect to the various boundary conditions.},
author = {Došlá, Zuzana, Došlý, Ondřej},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {quadratic functional; singular quadratic functional; periodic and antiperiodic boundary condition; conjugate point; coupled point; singularity condition; singular quadratic functionals; boundary conditions},
language = {eng},
number = {2},
pages = {219-237},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Singular quadratic functionals of one dependent variable},
url = {http://eudml.org/doc/247703},
volume = {36},
year = {1995},
}
TY - JOUR
AU - Došlá, Zuzana
AU - Došlý, Ondřej
TI - Singular quadratic functionals of one dependent variable
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 2
SP - 219
EP - 237
AB - 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 coupled point and singularity condition. The paper also includes two comparison theorems for coupled points with respect to the various boundary conditions.
LA - eng
KW - quadratic functional; singular quadratic functional; periodic and antiperiodic boundary condition; conjugate point; coupled point; singularity condition; singular quadratic functionals; boundary conditions
UR - http://eudml.org/doc/247703
ER -
References
top- Coppel W.A., Disconjugacy, Lectures Notes in Math. 220 Springer Verlag, 1971. Zbl0224.34003MR0460785
- Došlá Z., Došlý O., On transformations of singular quadratic functionals corresponding to the equation , Arch. Math. 24 (1988), 75-82. (1988) MR0983225
- Došlá Z., Zezza P., Singular quadratic functionals with variable end point, Comment. Math. Univ. Carolinae 33 (1992), 411-425. (1992) MR1209284
- 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. (1994) MR1386044
- 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. (1951) Zbl0045.20806MR0046590
- Leighton W., Morse M., Singular quadratic functionals, Trans. Amer. Math. Soc. 40 (1936), 252-286. (1936) Zbl0015.02701MR1501873
- Leighton W., Principal quadratic functionals, Trans. Amer. Math. Soc. 67 (1949), 253-274. (1949) Zbl0041.22404MR0034535
- Leighton W., Martin A.D., Quadratic functionals with a singular end point, Trans. Amer. Math. Soc. 78 (1955), 98-128. (1955) Zbl0064.35401MR0066570
- Reid W.T., Sturmian theory for ordinary differential equations, Springer Verlag, 1980. Zbl0459.34001MR0606199
- Stein J., Hilbert space and variational methods for singular selfadjoint systems of differential equations, Bull. Amer. Math. Soc. 80 (1974), 744-747. (1974) Zbl0289.34039MR0417486
- Tomastik E.C., Singular quadratic functionals of dependent variables, Trans. Amer. Math. Soc. 124 (1966), 60-76. (1966) Zbl0161.09503MR0196556
- Tomastik E.C., Principal quadratic functionals, Trans. Amer. Math. Soc. 218 (1976), 297-309. (1976) Zbl0346.49013MR0405208
- Zeidan V., Zezza P., Coupled points in the calculus of variations and applications to periodic problems, Trans. Amer. Math. Soc. 315 (1989), 323-335. (1989) Zbl0677.49020MR0961599
- 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. MR0956284
- Zezza P., The Jacobi condition for elliptic forms in Hilbert spaces,, JOTA 76 (1993), 357-380. (1993) MR1203907
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.