Solutions to nonlocal evolution equations governed by non-autonomous forms and demicontinuous nonlinearities

Abstract

We deal with the existence of solutions having L^2-regularity for a class of non-autonomous evolution equations. Associated with the equation, a general non-local condition is studied. The technique we used combines a finite dimensional reduction together with the Leray–Schauder continuation principle. This approach permits to consider a wide class of nonlinear terms by allowing demicontinuity assumptions on the nonlinearity.