Almost periodic generalized solutions of differential equations

Chikh Bouzar; Fethia Ouikene

Mathematica Bohemica (2021)

  • Volume: 146, Issue: 2, page 121-131
  • ISSN: 0862-7959

Abstract

top
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.

How to cite

top

Bouzar, Chikh, and Ouikene, Fethia. "Almost periodic generalized solutions of differential equations." Mathematica Bohemica 146.2 (2021): 121-131. <http://eudml.org/doc/297591>.

@article{Bouzar2021,
abstract = {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.},
author = {Bouzar, Chikh, Ouikene, Fethia},
journal = {Mathematica Bohemica},
keywords = {almost periodicity; generalized solution; ordinary differential equations},
language = {eng},
number = {2},
pages = {121-131},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Almost periodic generalized solutions of differential equations},
url = {http://eudml.org/doc/297591},
volume = {146},
year = {2021},
}

TY - JOUR
AU - Bouzar, Chikh
AU - Ouikene, Fethia
TI - Almost periodic generalized solutions of differential equations
JO - Mathematica Bohemica
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 146
IS - 2
SP - 121
EP - 131
AB - 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.
LA - eng
KW - almost periodicity; generalized solution; ordinary differential equations
UR - http://eudml.org/doc/297591
ER -

References

top
  1. Benmeriem, K., Bouzar, C., Generalized Gevrey ultradistributions, New York J. Math. 15 (2009), 37-72. (2009) Zbl1177.46031MR2481307
  2. Benmeriem, K., Bouzar, C., An algebra of generalized Roumieu ultradistributions, Rend. Semin. Mat., Univ. Politec. Torino 70 (2012), 101-109. (2012) Zbl1307.46032MR3305535
  3. Bouzar, C., Khalladi, M. T., Almost periodic generalized functions, Novi Sad J. Math. 41 (2011), 33-42. (2011) Zbl1265.46063MR2932762
  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. (2012) Zbl1304.46037MR3305536
  5. Bouzar, C., Ouikene, M. T. F., 10.2298/fil1917407b, Filomat 33 (2019), 5407-5425. (2019) MR4055607DOI10.2298/fil1917407b
  6. Cioranescu, I., 10.2307/2159304, Proc. Am. Math. Soc. 116 (1992), 127-134. (1992) Zbl0765.46021MR1111214DOI10.2307/2159304
  7. Corduneanu, C., 10.1007/978-0-387-09819-7, Springer, New York (2009). (2009) Zbl1163.34002MR2460203DOI10.1007/978-0-387-09819-7
  8. Debrouwere, A., Vernaeve, H., Vindas, J., 10.1007/s00605-017-1066-6, Monatsh. Math. 186 (2018), 407-438. (2018) Zbl1403.46033MR3817011DOI10.1007/s00605-017-1066-6
  9. Erlacher, E., Grosser, M., 10.1007/978-3-0348-0585-8_13, Pseudo-Differential Operators, Generalized Functions and Asymptotics. Oper. Theory Adv. Appl. 231 Birkhäuser/Springer, Basel (2013), 253-270 S. Molahajloo et al. (2013) Zbl1275.46025MR3075942DOI10.1007/978-3-0348-0585-8_13
  10. Fink, A. M., 10.1007/BFb0070324, Lecture Notes in Mathematics 377. Springer, Berlin (1974). (1974) Zbl0325.34039MR0460799DOI10.1007/BFb0070324
  11. Hale, J. K., Lunel, S. M. Verduyn, 10.1007/978-1-4612-4342-7, Applied Mathematical Sciences 99. Springer, New York (1993). (1993) Zbl0787.34002MR1243878DOI10.1007/978-1-4612-4342-7
  12. Komatsu, H., Ultradistributions. I. Structure theorems and a characterization, J. Fac. Sci., Univ. Tokyo, Sect. I A 20 (1973), 25-105. (1973) Zbl0258.46039MR0320743
  13. Kunzinger, M., Oberguggenberger, M., Steinbauer, R., Vickers, J. A., 10.1023/B:ACAP.0000013815.32211.24, Acta Appl. Math. 80 (2004), 221-241. (2004) Zbl1060.46030MR2035508DOI10.1023/B:ACAP.0000013815.32211.24
  14. Ligęza, J., 10.21136/MB.1998.126067, Math. Bohem. 123 (1998), 301-316. (1998) Zbl0937.34003MR1645454DOI10.21136/MB.1998.126067
  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). (1992) Zbl0818.46036MR1187755
  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). (1966) Zbl0149.09501MR0209834
  17. Wiener, J., 10.1142/1860, World Scientific, Singapore (1993). (1993) Zbl0874.34054MR1233560DOI10.1142/1860

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.