Geodesic
Discrete singular functionals
Archivum mathematicum, Tome 41 (2005) no. 3, pp. 339-347 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 39A12, 49J45, 49N10
Keywords: difference equation; half-linear equation; functional; singular functional 
@article{ARM_2005_41_3_a8,
     author = {Ma\v{r}{\'\i}k, Robert},
     title = {Discrete singular functionals},
     journal = {Archivum mathematicum},
     pages = {339--347},
     year = {2005},
     volume = {41},
     number = {3},
     mrnumber = {2188388},
     zbl = {1122.39303},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2005_41_3_a8/}
}
TY  - JOUR
AU  - Mařík, Robert
TI  - Discrete singular functionals
JO  - Archivum mathematicum
PY  - 2005
SP  - 339
EP  - 347
VL  - 41
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/ARM_2005_41_3_a8/
LA  - en
ID  - ARM_2005_41_3_a8
ER  - 
%0 Journal Article
%A Mařík, Robert
%T Discrete singular functionals
%J Archivum mathematicum
%D 2005
%P 339-347
%V 41
%N 3
%U http://geodesic.mathdoc.fr/item/ARM_2005_41_3_a8/
%G en
%F ARM_2005_41_3_a8
Mařík, Robert. Discrete singular functionals. Archivum mathematicum, Tome 41 (2005) no. 3, pp. 339-347. http://geodesic.mathdoc.fr/item/ARM_2005_41_3_a8/

[1] Došlá Z., Došlý O.: Singular quadratic functionals of one dependent variable. Comment. Math. Univ. Carolinae 36 (1995), 219–237. | MR | Zbl

[2] Hartman P.: Ordinary differential equations. J. Wiley & Sons, New York, (1964). | MR | Zbl

[3] Kelley W. G., Peterson A. C.: Difference equations - An introduction with applications. Academic Press (1991). | MR | Zbl

[4] Leighton W.: Principal quadratic functionals. Trans. Amer. Math. Soc. 67 (1949), 253–274. | MR | Zbl

[5] Leighton W., Martin A. D.: Quadratic functionals with a singular end point. Trans. Amer. Math. Soc. 78 (1955), 98–128. | MR | Zbl

[6] Leighton W., Morse M.: Singular quadratic functionals. Trans. Amer. Math. Soc. 40 (1936), 252-286. | MR | Zbl

[7] Mařík R.: Nonnegativity of functionals corresponding to the second order half-linear differential equation. Arch. Math. (Brno) 35 (1999), 155–164. | MR

[8] Mařík R.: Comparison theorems for half-linear second order difference equations. Arch. Math. (Brno) 36 (2000), 513–518. | MR | Zbl

[9] Řehák P.: Oscillatory properties of second order half–linear difference equations. Czech. Math. J. 51, No. 2 (2001), 303–321. | MR