Singular quadratic functionals of one dependent variable

Zuzana Došlá; Ondřej Došlý

Commentationes Mathematicae Universitatis Carolinae (1995)

  • Volume: 36, Issue: 2, page 219-237
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Došlá, 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

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  11. Tomastik E.C., Singular quadratic functionals of n dependent variables, Trans. Amer. Math. Soc. 124 (1966), 60-76. (1966) Zbl0161.09503MR0196556
  12. Tomastik E.C., Principal quadratic functionals, Trans. Amer. Math. Soc. 218 (1976), 297-309. (1976) Zbl0346.49013MR0405208
  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. (1989) Zbl0677.49020MR0961599
  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. MR0956284
  15. Zezza P., The Jacobi condition for elliptic forms in Hilbert spaces,, JOTA 76 (1993), 357-380. (1993) MR1203907

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