Research Article
BibTex RIS Cite

Reduction method for functional nonconvex differential inclusions

Year 2021, , 6 - 14, 29.04.2021
https://doi.org/10.47087/mjm.853437

Abstract

Our aim in this paper is to present a reduction method that solves first order functional differential inclusion in the nonconvex case. This approach is based on a discretization of the time interval, a construction of approximate solutions by reducing the problem to a problem without delay and an application of known results in this case. We generalises earlier results, the right hand side of the inclusion has nonconvex values and satisfies a linear growth condition instead to be integrably bounded. The lack of convexity is replaced by the topological properties of decomposable sets, that represents a good alternative in the absence of convexity.

Supporting Institution

Research supported by the General direction of scientific research and technological development (DGRSDT), Algeria

Project Number

PRFU No. C00L03UN180120180001.

References

  • D. Affane and M. F. Yarou; Second-order perturbed state-dependent sweeping process with subsmooth sets, In: Zeidan D., Padhi S., Burqan A., Ueberholz P. (eds) computational Mathematics and Applications. Forum for Interdisciplinary Mathematics. Springer, Singapore (2020) 147-169.
  • D. Affane and M. F. Yarou; General second order functional differential inclusions driven by the sweeping process with subsmooth sets, J. Nonlin. Funct. Anal. Article ID 26 (2020) 1-18.
  • D. Affane and M. F. Yarou; Unbounded perturbation to time-dependent subdifferential operators with delay, Electr. J. Math. Anal. Appl. 02(8) (2020) 209-219.
  • D. Affane and M. F. Yarou; Fixed point approach for differential inclusions governed by subdifferential operators, AIP Conference Proceedings 2183, 060002 (2019); https : // doi.org /10.1063 / 1. 5136157
  • N. Fetouci and M. F. Yarou; A fixed point approach for a differential inclusion governed by the subdifferential of PLN functions, AIP Conference Proceedings 2183, 060005 (2019); https://doi.org/10.1063/1.5136160
  • J. P. Aubin, A. Cellina; Differential inclusions, Springer-Verlag, (1984).
  • M. Bounkhel and M. F. Yarou; Existence results for first and second order nonconvex sweeping process with delay, Portug. Math. 61 (2) (2004) 207-230.
  • C. Castaing, A. Salvadori and L. Thibault; Functional evolution equations governed by nonconvex sweeping process, J. Nonlin. Conv. Anal. 2(2) (2001) 217-241.
  • C. Castaing and M. Valadier; Convex Analysis and Measurable Multifunctions, Lecture Note in Math. 580, Springer, Berlin, (1997).
  • A. Fryszkowski; Continuous selections for a class of non-convex multivalued maps, Studia Math. 76(2) (1983) 163-174.
  • A. Fryszkowski; Existence of solutions of functional-differential inclusion in nonconvex case, Anal. Polonici Math. 45(2) (1985) 121-124.
  • A. Fryszkowski and L. Gorniewicz; Mixed semicontinuous mappings and their applications to differential inclusions, Set-Valued Anal. 8 (2000) 203-217.
  • M. F. Yarou; Reduction approach to second order perturbed state-dependent sweeping process, Crea. Math. Infor. 28 (02) (2019) 215-221.
Year 2021, , 6 - 14, 29.04.2021
https://doi.org/10.47087/mjm.853437

Abstract

Project Number

PRFU No. C00L03UN180120180001.

References

  • D. Affane and M. F. Yarou; Second-order perturbed state-dependent sweeping process with subsmooth sets, In: Zeidan D., Padhi S., Burqan A., Ueberholz P. (eds) computational Mathematics and Applications. Forum for Interdisciplinary Mathematics. Springer, Singapore (2020) 147-169.
  • D. Affane and M. F. Yarou; General second order functional differential inclusions driven by the sweeping process with subsmooth sets, J. Nonlin. Funct. Anal. Article ID 26 (2020) 1-18.
  • D. Affane and M. F. Yarou; Unbounded perturbation to time-dependent subdifferential operators with delay, Electr. J. Math. Anal. Appl. 02(8) (2020) 209-219.
  • D. Affane and M. F. Yarou; Fixed point approach for differential inclusions governed by subdifferential operators, AIP Conference Proceedings 2183, 060002 (2019); https : // doi.org /10.1063 / 1. 5136157
  • N. Fetouci and M. F. Yarou; A fixed point approach for a differential inclusion governed by the subdifferential of PLN functions, AIP Conference Proceedings 2183, 060005 (2019); https://doi.org/10.1063/1.5136160
  • J. P. Aubin, A. Cellina; Differential inclusions, Springer-Verlag, (1984).
  • M. Bounkhel and M. F. Yarou; Existence results for first and second order nonconvex sweeping process with delay, Portug. Math. 61 (2) (2004) 207-230.
  • C. Castaing, A. Salvadori and L. Thibault; Functional evolution equations governed by nonconvex sweeping process, J. Nonlin. Conv. Anal. 2(2) (2001) 217-241.
  • C. Castaing and M. Valadier; Convex Analysis and Measurable Multifunctions, Lecture Note in Math. 580, Springer, Berlin, (1997).
  • A. Fryszkowski; Continuous selections for a class of non-convex multivalued maps, Studia Math. 76(2) (1983) 163-174.
  • A. Fryszkowski; Existence of solutions of functional-differential inclusion in nonconvex case, Anal. Polonici Math. 45(2) (1985) 121-124.
  • A. Fryszkowski and L. Gorniewicz; Mixed semicontinuous mappings and their applications to differential inclusions, Set-Valued Anal. 8 (2000) 203-217.
  • M. F. Yarou; Reduction approach to second order perturbed state-dependent sweeping process, Crea. Math. Infor. 28 (02) (2019) 215-221.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Hanane Chouial 0000-0001-6599-9765

Mustapha Fateh Yarou 0000-0003-4083-1813

Project Number PRFU No. C00L03UN180120180001.
Publication Date April 29, 2021
Acceptance Date April 4, 2021
Published in Issue Year 2021

Cite

APA Chouial, H., & Yarou, M. F. (2021). Reduction method for functional nonconvex differential inclusions. Maltepe Journal of Mathematics, 3(1), 6-14. https://doi.org/10.47087/mjm.853437
AMA Chouial H, Yarou MF. Reduction method for functional nonconvex differential inclusions. Maltepe Journal of Mathematics. April 2021;3(1):6-14. doi:10.47087/mjm.853437
Chicago Chouial, Hanane, and Mustapha Fateh Yarou. “Reduction Method for Functional Nonconvex Differential Inclusions”. Maltepe Journal of Mathematics 3, no. 1 (April 2021): 6-14. https://doi.org/10.47087/mjm.853437.
EndNote Chouial H, Yarou MF (April 1, 2021) Reduction method for functional nonconvex differential inclusions. Maltepe Journal of Mathematics 3 1 6–14.
IEEE H. Chouial and M. F. Yarou, “Reduction method for functional nonconvex differential inclusions”, Maltepe Journal of Mathematics, vol. 3, no. 1, pp. 6–14, 2021, doi: 10.47087/mjm.853437.
ISNAD Chouial, Hanane - Yarou, Mustapha Fateh. “Reduction Method for Functional Nonconvex Differential Inclusions”. Maltepe Journal of Mathematics 3/1 (April 2021), 6-14. https://doi.org/10.47087/mjm.853437.
JAMA Chouial H, Yarou MF. Reduction method for functional nonconvex differential inclusions. Maltepe Journal of Mathematics. 2021;3:6–14.
MLA Chouial, Hanane and Mustapha Fateh Yarou. “Reduction Method for Functional Nonconvex Differential Inclusions”. Maltepe Journal of Mathematics, vol. 3, no. 1, 2021, pp. 6-14, doi:10.47087/mjm.853437.
Vancouver Chouial H, Yarou MF. Reduction method for functional nonconvex differential inclusions. Maltepe Journal of Mathematics. 2021;3(1):6-14.

Creative Commons License
The published articles in MJM are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

ISSN 2667-7660