Nonlocal semilinear evolution inclusions with time lag

Abstract

In this paper, nonautonomous semilinear evolution inclusions with time lag and nonlocal initial conditions are studied. We define the so-called limit and weak solutions. We prove the existence of solutions when the multivalued part of the right-hand side and the initial functions are Lipschitz under natural conditions on the Lipschitz constants. Afterwards, under the same conditions, a variant of the important in optimal control relaxation theorem is proved.