On certain classes of functional inclusions with causal operators in Banach spaces (Q531667)

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.