| Title:
|
Discrete singular functionals (English) |
| Author:
|
Mařík, Robert |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
41 |
| Issue:
|
3 |
| Year:
|
2005 |
| Pages:
|
339-347 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
difference equation |
| Keyword:
|
half-linear equation |
| Keyword:
|
functional |
| Keyword:
|
singular functional |
| MSC:
|
39A12 |
| MSC:
|
49J45 |
| MSC:
|
49N10 |
| idZBL:
|
Zbl 1122.39303 |
| idMR:
|
MR2188388 |
| . |
| Date available:
|
2008-06-06T22:46:27Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107963 |
| . |
| Reference:
|
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| Reference:
|
[2] Hartman P.: Ordinary differential equations.J. Wiley & Sons, New York, (1964). Zbl 0125.32102, MR 0171038 |
| Reference:
|
[3] Kelley W. G., Peterson A. C.: Difference equations - An introduction with applications.Academic Press (1991). Zbl 0733.39001, MR 1142573 |
| Reference:
|
[4] Leighton W.: Principal quadratic functionals.Trans. Amer. Math. Soc. 67 (1949), 253–274. Zbl 0041.22404, MR 0034535 |
| Reference:
|
[5] Leighton W., Martin A. D.: Quadratic functionals with a singular end point.Trans. Amer. Math. Soc. 78 (1955), 98–128. Zbl 0064.35401, MR 0066570 |
| Reference:
|
[6] Leighton W., Morse M.: Singular quadratic functionals.Trans. Amer. Math. Soc. 40 (1936), 252-286. Zbl 0015.02701, MR 1501873 |
| Reference:
|
[7] Mařík R.: Nonnegativity of functionals corresponding to the second order half-linear differential equation.Arch. Math. (Brno) 35 (1999), 155–164. MR 1711728 |
| Reference:
|
[8] Mařík R.: Comparison theorems for half-linear second order difference equations.Arch. Math. (Brno) 36 (2000), 513–518. Zbl 1090.39500, MR 1822821 |
| Reference:
|
[9] Řehák P.: Oscillatory properties of second order half–linear difference equations.Czech. Math. J. 51, No. 2 (2001), 303–321. MR 1844312 |
| . |
