| Title:
|
Some dynamic inequalities applicable to partial integrodifferential equations on time scales (English) |
| Author:
|
Pachpatte, Deepak B. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
51 |
| Issue:
|
3 |
| Year:
|
2015 |
| Pages:
|
143-152 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The main objective of the paper is to study explicit bounds of certain dynamic integral inequalities on time scales. Using these inequalities we prove the uniqueness of some partial integrodifferential equations on time scales. (English) |
| Keyword:
|
explicit bounds |
| Keyword:
|
integral inequality |
| Keyword:
|
dynamic equations |
| Keyword:
|
time scales |
| MSC:
|
26E70 |
| MSC:
|
34N05 |
| idZBL:
|
Zbl 06487026 |
| idMR:
|
MR3397267 |
| DOI:
|
10.5817/AM2015-3-143 |
| . |
| Date available:
|
2015-09-09T09:43:57Z |
| Last updated:
|
2016-04-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144425 |
| . |
| Reference:
|
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| Reference:
|
[2] Andras, S., Meszaros, A.: Wendroff type inequalities on time scales via Picard operators.Math. Inequal. Appl. 17 (1) (2013), 159–174. Zbl 1262.35006, MR 3060387 |
| Reference:
|
[3] Bohner, M., Peterson, A.: Dynamic equations on time scales.Birkhauser Boston–Berlin, 2001. Zbl 0993.39010, MR 1843232 |
| Reference:
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[4] Bohner, M., Peterson, A.: Advances in dynamic equations on time scales.Birkhauser Boston–Berlin, 2003. Zbl 1025.34001, MR 1962542 |
| Reference:
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[5] Hilger, S.: Analysis on measure chain – A unified approch to continuous and discrete calculus.Results Math. 18 (1990), 18–56. MR 1066641, 10.1007/BF03323153 |
| Reference:
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[6] Menga, F., Shaoa, J.: Some new Volterra–Fredholm type dynamic integral inequalities on time scales.Appl. Math. Comput. 223 (2013), 444–451. MR 3116277, 10.1016/j.amc.2013.08.025 |
| Reference:
|
[7] Pachpatte, D.B.: Explicit estimates on integral inequalities with time scale.J. Inequal. Pure Appl. Math. 7 (4) (2006), Article 143. Zbl 1182.26068, MR 2268597 |
| Reference:
|
[8] Pachpatte, D.B.: Properties of solutions to nonlinear dynamic integral equations on time scales.Electron. J. Differential Equations 2008 (2008), no. 130, 1–8. Zbl 1165.39017, MR 2448891 |
| Reference:
|
[9] Pachpatte, D.B.: Integral inequalities for partial dynamic equations on time scales.Electron. J. Differential Equations 2012 (2012), no. 50, 1–7. Zbl 1238.26032, MR 2927786 |
| Reference:
|
[10] Pachpatte, D.B.: Properties of some partial dynamic equations on time scales.Internat. J. Partial Differential Equations 2013 (2013), 9pp., Art. ID 345697. |
| Reference:
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[11] Saker, S. H.: Some nonlinear dynamic inequalities on time scales and applications.J. Math. Inequalities 4 (2010), 561–579. Zbl 1207.26034, MR 2777272, 10.7153/jmi-04-50 |
| Reference:
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[12] Saker, S.H.: Bounds of double integral dynamic inequalities in two independent variables on time scales.Discrete Dynamics in Nature and Society (2011), Art. 732164. Zbl 1238.26033, MR 2861953 |
| Reference:
|
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| Reference:
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| . |
