Implicit differential inclusions in reflexive smooth Banach spaces (Q2845552)
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scientific article; zbMATH DE number 6203546
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Implicit differential inclusions in reflexive smooth Banach spaces |
scientific article; zbMATH DE number 6203546 |
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Implicit differential inclusions in reflexive smooth Banach spaces (English)
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2 September 2013
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uniformly smooth and uniformly convex Banach spaces
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implicit convex sweeping process
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generalized projection
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duality mapping
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The author considers the initial value problem for implicit differential inclusions NEWLINE\[NEWLINE0\in G(t, u(t), \dot u(t)) \quad \text{a.e. \,\, on}\quad [0,T], \quad u(0)=x_0,NEWLINE\]NEWLINE where \(G:[0,T]\times {\mathbb R}^n\times {\mathbb R}^n \to {\mathcal P}({\mathbb R}^n)\) is a set valued mapping. Existence results are proved when \(G\) has the general form \(G(t,x,y)=N(C(t),y)+F(t,x)+y\) and the space is a separable, reflexive, smooth Banach space. A positive answer is given to a question of \textit{Z. Ding} [Proc. Am. Math. Soc. 124, No. 3, 745--749 (1996; Zbl 0851.34013)].
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