Discrete singular functionals

Robert Mařík

Archivum Mathematicum (2005)

  • Volume: 041, Issue: 3, page 339-347
  • ISSN: 0044-8753

Abstract

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In the paper the discrete version of the Morse’s singularity condition is established. This condition ensures that the discrete functional over the unbounded interval is positive semidefinite on the class of the admissible functions. Two types of admissibility are considered.

How to cite

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Mařík, Robert. "Discrete singular functionals." Archivum Mathematicum 041.3 (2005): 339-347. <http://eudml.org/doc/249490>.

@article{Mařík2005,
abstract = {In the paper the discrete version of the Morse’s singularity condition is established. This condition ensures that the discrete functional over the unbounded interval is positive semidefinite on the class of the admissible functions. Two types of admissibility are considered.},
author = {Mařík, Robert},
journal = {Archivum Mathematicum},
keywords = {difference equation; half-linear equation; functional; singular functional; difference equation; half-linear equation; functional},
language = {eng},
number = {3},
pages = {339-347},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Discrete singular functionals},
url = {http://eudml.org/doc/249490},
volume = {041},
year = {2005},
}

TY - JOUR
AU - Mařík, Robert
TI - Discrete singular functionals
JO - Archivum Mathematicum
PY - 2005
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 041
IS - 3
SP - 339
EP - 347
AB - In the paper the discrete version of the Morse’s singularity condition is established. This condition ensures that the discrete functional over the unbounded interval is positive semidefinite on the class of the admissible functions. Two types of admissibility are considered.
LA - eng
KW - difference equation; half-linear equation; functional; singular functional; difference equation; half-linear equation; functional
UR - http://eudml.org/doc/249490
ER -

References

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  1. Došlá Z., Došlý O., Singular quadratic functionals of one dependent variable, Comment. Math. Univ. Carolinae 36 (1995), 219–237. (1995) Zbl0838.34036MR1357523
  2. Hartman P., Ordinary differential equations, J. Wiley & Sons, New York, (1964). (1964) Zbl0125.32102MR0171038
  3. Kelley W. G., Peterson A. C., Difference equations - An introduction with applications, Academic Press (1991). (1991) Zbl0733.39001MR1142573
  4. Leighton W., Principal quadratic functionals, Trans. Amer. Math. Soc. 67 (1949), 253–274. (1949) Zbl0041.22404MR0034535
  5. Leighton W., Martin A. D., Quadratic functionals with a singular end point, Trans. Amer. Math. Soc. 78 (1955), 98–128. (1955) Zbl0064.35401MR0066570
  6. Leighton W., Morse M., Singular quadratic functionals, Trans. Amer. Math. Soc. 40 (1936), 252-286. (1936) Zbl0015.02701MR1501873
  7. Mařík R., Nonnegativity of functionals corresponding to the second order half-linear differential equation, Arch. Math. (Brno) 35 (1999), 155–164. (1999) MR1711728
  8. Mařík R., Comparison theorems for half-linear second order difference equations, Arch. Math. (Brno) 36 (2000), 513–518. Zbl1090.39500MR1822821
  9. Řehák P., Oscillatory properties of second order half–linear difference equations, Czech. Math. J. 51, No. 2 (2001), 303–321. MR1844312

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