The authors present the existence of integral solutions and extremal integral solutions for the following problem
where are a multivalued maps, is the family of all nonempty subsets of , is a nondensely defined closed linear operator on , , ,
, , and stand for the right and the left limits of at , respectively.
For any function defined on and any , refers to the element of such that
thus the function represents the history of the state from time up to the present time . Also the controllability of above problem are investigated. An examples is presented.