Nonlocal differential equations with multivalued perturbations in Banach spaces (Q949709)

The authors study the following nonlocal initial value problem \[ \begin{cases} u'(t)\in Au(t)+F(t,u(t)),&\;t\in[0,T],\\ u(0)=g(u),\end{cases} \] where \(A:D(A)\subseteq E\rightarrow E\) is the densely defined generator of a compact semigroup for \(t>0\) in a real Banach space \(E\); \(F\) is an upper-Carathéodory multifunction; \(g:C([0,T])\rightarrow E\) is a given function. As the main result, a theorem on the existence of mild solutions for this problem is proved. An example illustrating the abstract result is also presented.