On semilinear differential inclusions with lower semicontinuous nonlinearities (Q1408581)

The authors study a Cauchy problem governed by the semilinear differential inclusion in a Banach space \[ x'(t)\in Ax(t)+F(t,x(t)), \;t\in [0,a], \] where the linear operator \(A:D(A)\subset E\to E\) is the infinitesimal generator of a strongly continuous semigroup and \(F\) is a lower semicontinuous multifunction not necessarily convex-valued. In this general situation, the authors prove the existence of a mild solution to the problem. They make use of a technique developed by themselves and based on the notion of measure of noncompactness.