Quadratic functionals with a variable singular end point

Zuzana Došlá; PierLuigi Zezza

Commentationes Mathematicae Universitatis Carolinae (1992)

  • Volume: 33, Issue: 3, page 411-425
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Došlá, Zuzana, and Zezza, PierLuigi. "Quadratic functionals with a variable singular end point." Commentationes Mathematicae Universitatis Carolinae 33.3 (1992): 411-425. <http://eudml.org/doc/247380>.

@article{Došlá1992,
abstract = {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.},
author = {Došlá, Zuzana, Zezza, PierLuigi},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {quadratic functional; singular quadratic functional; Euler-Lagrange equation; conjugate point; coupled point; singularity condition; singular quadratic functional; Euler-Lagrange equation; conjugate point; coupled point; necessary and sufficient conditions},
language = {eng},
number = {3},
pages = {411-425},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Quadratic functionals with a variable singular end point},
url = {http://eudml.org/doc/247380},
volume = {33},
year = {1992},
}

TY - JOUR
AU - Došlá, Zuzana
AU - Zezza, PierLuigi
TI - Quadratic functionals with a variable singular end point
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1992
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 33
IS - 3
SP - 411
EP - 425
AB - 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.
LA - eng
KW - quadratic functional; singular quadratic functional; Euler-Lagrange equation; conjugate point; coupled point; singularity condition; singular quadratic functional; Euler-Lagrange equation; conjugate point; coupled point; necessary and sufficient conditions
UR - http://eudml.org/doc/247380
ER -

References

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  1. Morse M., Leighton W., Singular quadratic functionals, Trans. Amer. Math. Soc. 40 (1936), 252-286. (1936) Zbl0015.02701MR1501873
  2. Leighton W., Principal quadratic functionals, Trans. Amer. Math. Soc. 67 (1949), 253-274. (1949) Zbl0041.22404MR0034535
  3. Leighton W., Martin A.D., Quadratic functionals with a singular end point, Trans. Amer. Math. Soc. 78 (1955), 98-128. (1955) Zbl0064.35401MR0066570
  4. Reid W.T., Sturmian theory for ordinary differential equations, Springer-Verlag 1980. Zbl0459.34001MR0606199
  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. (1989) Zbl0677.49020MR0961599
  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. MR0956284
  7. Zezza P., The Jacobi condition for elliptic forms in Hilbert spaces, JOTA 76 (1993). (1993) MR1203907
  8. Zezza P., Došlá Z., Coupled points in the calculus of variations and optimal control theory via the quadratic form theory, preprint. 
  9. Coppel W.A., Disconjugacy, Lecture Notes in Math. 220, Springer-Verlag, Berlin-Heidelberg, 1971. Zbl0224.34003MR0460785

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