A viability result for Carathéodory non-convex differential inclusion in Banach spaces

• Autorzy: Charradi Nabil , Sajid Saïd

Identyfikatory

DOI

10.7494/OpMath.2023.43.5.621

• Języki publikacji: EN

Abstrakty

EN

This paper deals with the existence of solutions to the following differential inclusion: x˙ (t) ∈ F(t, x(t)) a.e. on [0, T[ and x(t) ∈ K, for all t ∈ [0, T], where F : [0, T] × K → 2E is a Carathéodory multifunction and K is a closed subset of a separable Banach space E.

Słowa kluczowe

EN

viability; measurable multifunction; selection; Carathéodory multifunction

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2023
• Tom: Vol. 43, no. 5
• Strony: 621--632
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Charradi Nabil

• University Hassan II of Casablanca, Department of Mathematics, FSTM, Mohammedia, 28820, Morocco

• https://orcid.org/0000-0002-6382-8396

autor

Sajid Saïd

• University Hassan II of Casablanca, Department of Mathematics, FSTM, Mohammedia, 28820, Morocco

• https://orcid.org/0000-0002-4377-5928

Bibliografia

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• [2] M. Aitalioubrahim, Viability result for semilinear functional differential inclusions in Banach spaces, Carpathian Math. Publ. 13 (2021), no. 2, 395–404.
• [3] C. Castaing, M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics, vol. 580, Springer-Verlag, Berlin–Heidelberg–New York, 1977.
• [4] Q. Dong, G. Li, Viability for semilinear differential equations with infinite delay, Mathematics 2016, 4(4), 64.
• [5] Z. Fan, G. Li, Existence results for semilinear differential inclusions, Bull. Austral. Math. Soc. 76 (2007), no. 2, 227–241.
• [6] T.X.D. Ha, Existence of viable solutions for nonconvex valued differential inclusions in Banach spaces, Portugal. Math. 52 (1995), Fasc. 2, 241–250.
• [7] G. Haddad, Monotone trajectories for functional differential inclusions, J. Diff. Equations 42 (1981), no. 1, 1–24.
• [8] G. Haddad, Monotone trajectories of differential inclusions and functional differential inclusions with memory, Israel J. Math. 39 (1981), 83–100.
• [9] M. Larrieu, Invariance d’un fermé pour un champ de vecteurs de Carathéodory, Pub. Math. de Pau, 1981.
• [10] V. Lupulescu, M. Necula, Viability and local invariance for non-convex semilinear differential inclusions, Nonlinear Funct. Anal. Appl. 9 (2004), no. 3, 495–512.
• [11] V. Lupulescu, M. Necula, A viability result for nonconvex semilinear functional differential inclusions, Discuss. Math. Differ. Incl. Control Optim. 25 (2005), 109–128.
• [12] V. Lupulescu, M. Necula, A viable result for nonconvex differential inclusions with memory, Port. Math. (N.S.) 63 (2006), no. 3, 335–349.
• [13] Q.J. Zhu, On the solution set of differential inclusions in Banach space, J. Differential Equations 93 (1991), no. 2, 213–237.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)