Existence results for initial value problems for neutral functional differential inclusions in Banach spaces
The author proves an existence result for the following initial value problem \[ \frac{d}{dx}[x(t)-g(t,x_{t})] \in F(t,x_{t}), \enskip t\in I, \] \[ x_0=\phi, \] where \(\phi \in C([-r,0],E)\), \(r>0\), \(E\) is a Banach space, \(I=[0,\omega]\), \(g:I\times C([-r,0],E)\to E\) is a continuous function and \(F\) an appropriate multimapping. The proof is based on an application of the topological transversality for multimappings. An application of the main result is also given for the optimal control of a system described by an integrodifferential equation.
neutral functional differential inclusions in Banach spaces
scientific article; zbMATH DE number 5354275