An Existence Result for a Class of Delay Inclusions Involving Measures, Subjected to Nonlocal Initial Data

In this paper, we prove an existence result for L ∞ -solutions for a class of semilinear delay evolution inclusions with measures and subjected to nonlocal initial conditions of the form d u ( t ) = { A u ( t ) + f ( t ) } d t + d h ( t ) , t ∈ R + , f ( t ) ∈ F ( t , u t ) , t ∈ R + , u ( t ) = g ( u ) ( t ) , t ∈ [ - τ , 0 ] . Here τ ≥ 0 , X is a Banach space, A : D ( A ) ⊆ X → X is the infinitesimal generator of a C 0 -semigroup, F : R + × R ( [ - τ , 0 ] ; X ) ⇝ X is a u.s.c. multifunction with nonempty, convex and weakly compact values, h ∈ B V loc ( R + ; X ) and the function g : R b ( R + ; X ) → R ( [ - τ , 0 ] ; X ) is nonexpansive.