Opuscula Math. 43, no. 5 (2023), 621-632
https://doi.org/10.7494/OpMath.2023.43.5.621
Opuscula Mathematica
A viability result for Carathéodory non-convex differential inclusion in Banach spaces
Abstract. This paper deals with the existence of solutions to the following differential inclusion: \(\dot{x}(t)\in F(t,x(t))\) a.e. on \([0, T[\) and \(x(t)\in K\), for all \(t \in [0, T]\), where \(F: [0, T]\times K \rightarrow 2^E\) is a Carathéodory multifunction and \(K\) is a closed subset of a separable Banach space \(E\).
Keywords: viability, measurable multifunction, selection, Carathéodory multifunction.
Mathematics Subject Classification: 34A60, 28B20.
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- Nabil Charradi
https://orcid.org/0000-0002-6382-8396- University Hassan II of Casablanca, Department of Mathematics, FSTM, Mohammedia, 28820, Morocco
- Saïd Sajid (corresponding author)
- https://orcid.org/0000-0002-4377-5928
- University Hassan II of Casablanca, Department of Mathematics, FSTM, Mohammedia, 28820, Morocco
- Communicated by P.A. Cojuhari.
- Received: 2023-03-17.
- Revised: 2023-04-24.
- Accepted: 2023-05-14.
- Published online: 2023-06-24.
