| Title:
|
Almost periodic generalized solutions of differential equations (English) |
| Author:
|
Bouzar, Chikh |
| Author:
|
Ouikene, Fethia |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
146 |
| Issue:
|
2 |
| Year:
|
2021 |
| Pages:
|
121-131 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper aims to study systems of linear ordinary differential equations in the context of an algebra of almost periodic generalized ultradistributions. Conditions on the existence of generalized solutions are given. (English) |
| Keyword:
|
almost periodicity |
| Keyword:
|
generalized solution |
| Keyword:
|
ordinary differential equations |
| MSC:
|
34C27 |
| MSC:
|
46F30 |
| DOI:
|
10.21136/MB.2020.0054-19 |
| . |
| Date available:
|
2021-05-20T13:51:46Z |
| Last updated:
|
2021-06-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148927 |
| . |
| Reference:
|
[1] Benmeriem, K., Bouzar, C.: Generalized Gevrey ultradistributions.New York J. Math. 15 (2009), 37-72. Zbl 1177.46031, MR 2481307 |
| Reference:
|
[2] Benmeriem, K., Bouzar, C.: An algebra of generalized Roumieu ultradistributions.Rend. Semin. Mat., Univ. Politec. Torino 70 (2012), 101-109. Zbl 1307.46032, MR 3305535 |
| Reference:
|
[3] Bouzar, C., Khalladi, M. T.: Almost periodic generalized functions.Novi Sad J. Math. 41 (2011), 33-42. Zbl 1265.46063, MR 2932762 |
| Reference:
|
[4] Bouzar, C., Khalladi, M. T.: Linear differential equations in the algebra of almost periodic generalized functions.Rend. Semin. Mat., Univ. Politec. Torino 70 (2012), 111-120. Zbl 1304.46037, MR 3305536 |
| Reference:
|
[5] Bouzar, C., Ouikene, M. T. F.: Almost periodic generalized ultradistributions.Filomat 33 (2019), 5407-5425. MR 4055607, 10.2298/fil1917407b |
| Reference:
|
[6] Cioranescu, I.: The characterization of the almost periodic ultradistributions of Beurling type.Proc. Am. Math. Soc. 116 (1992), 127-134. Zbl 0765.46021, MR 1111214, 10.2307/2159304 |
| Reference:
|
[7] Corduneanu, C.: Almost Periodic Oscillations and Waves.Springer, New York (2009). Zbl 1163.34002, MR 2460203, 10.1007/978-0-387-09819-7 |
| Reference:
|
[8] Debrouwere, A., Vernaeve, H., Vindas, J.: Optimal embeddings of ultradistributions into differential algebras.Monatsh. Math. 186 (2018), 407-438. Zbl 1403.46033, MR 3817011, 10.1007/s00605-017-1066-6 |
| Reference:
|
[9] Erlacher, E., Grosser, M.: Ordinary differential equations in algebras of generalized functions.Pseudo-Differential Operators, Generalized Functions and Asymptotics. Oper. Theory Adv. Appl. 231 Birkhäuser/Springer, Basel (2013), 253-270 S. Molahajloo et al. Zbl 1275.46025, MR 3075942, 10.1007/978-3-0348-0585-8_13 |
| Reference:
|
[10] Fink, A. M.: Almost Periodic Differential Equations.Lecture Notes in Mathematics 377. Springer, Berlin (1974). Zbl 0325.34039, MR 0460799, 10.1007/BFb0070324 |
| Reference:
|
[11] Hale, J. K., Lunel, S. M. Verduyn: Introduction to Functional-Differential Equations.Applied Mathematical Sciences 99. Springer, New York (1993). Zbl 0787.34002, MR 1243878, 10.1007/978-1-4612-4342-7 |
| Reference:
|
[12] Komatsu, H.: Ultradistributions. I. Structure theorems and a characterization.J. Fac. Sci., Univ. Tokyo, Sect. I A 20 (1973), 25-105. Zbl 0258.46039, MR 0320743 |
| Reference:
|
[13] Kunzinger, M., Oberguggenberger, M., Steinbauer, R., Vickers, J. A.: Generalized flows and singular ODEs on differentiable manifolds.Acta Appl. Math. 80 (2004), 221-241. Zbl 1060.46030, MR 2035508, 10.1023/B:ACAP.0000013815.32211.24 |
| Reference:
|
[14] Ligęza, J.: Remarks on generalized solutions of ordinary linear differential equations in the Colombeau algebra.Math. Bohem. 123 (1998), 301-316. Zbl 0937.34003, MR 1645454, 10.21136/MB.1998.126067 |
| Reference:
|
[15] Oberguggenberger, M.: Multiplication of Distributions and Applications to Partial Differential Equations.Pitman Research Notes in Mathematics Series 259. Longman Scientific & Technical, Harlow; John Wiley & Sons, New York (1992). Zbl 0818.46036, MR 1187755 |
| Reference:
|
[16] Schwartz, L.: Théorie des distributions.Publications de l'Institut de Mathématique de l'Université de Strasbourg, No. IX-X. Nouvelle édition, entièrement corrigée, refondue et augmentée. Hermann, Paris French (1966). Zbl 0149.09501, MR 0209834 |
| Reference:
|
[17] Wiener, J.: Generalized Solutions of Functional Differential Equations.World Scientific, Singapore (1993). Zbl 0874.34054, MR 1233560, 10.1142/1860 |
| . |
