Convergence of nonlinear evolution operators in Banach spaces (Q1059841)

Let X be a (real) Banach space, and \[ (*)\quad u'(t)\in A(t)u(t),\quad s<t<T,\quad u(s)=x, \] wherein \(0\leq s<T\); \(x\in \overline{D(A(s))};\) u(\(\cdot)\) stands for an X-valued unknown function on the interval [s,T]; u'(\(\cdot)\) represents a derivative of u; and \(\{A(t): t\in [0,T]\}\) is a family of nonlinear, possibly multivalued operators in X. The author establishes a theorem (concerning the convergence of nonlinear evolution operators) extending to the time-dependent case (*) the convergence results for nonlinear semigroups due to \textit{H. Brézis} and \textit{A. Pazy} [J. Funct. Anal. 9, 63-74 (1972; Zbl 0231.47036)] and others.