On certain classes of functional inclusions with causal operators in Banach spaces. (English) Zbl 1225.47082
The topological degree theory for condensing maps is used to get local and global existence results in \({\mathcal D}_h\) (\(0< h\leq T\)) of the abstract Cauchy problem (P) \(y\in g+{\mathcal S}\circ{\mathcal Q}(y[\psi])\). Here, \(\psi\in {\mathcal C}\), \(g\in {\mathcal D}_h\) are given functions, and \({\mathcal S}\), \({\mathcal Q}\) are causal operators.
Reviewer: Mihai Turinici (Iaşi)
MSC:
| 47J05 | Equations involving nonlinear operators (general) |
| 47H10 | Fixed-point theorems |
| 34K09 | Functional-differential inclusions |
| 34A60 | Ordinary differential inclusions |
Keywords:
causal operator; functional inclusion; Cauchy problem; functional differential inclusion; Volterra integro-differential inclusion; continuous dependence; measure of noncompactness; fixed point; topological degree; multivalued map; condensing mapReferences:
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