On abstract differential equations with state dependent non-local conditions

In this paper we introduce the concept of “state dependent nonlocal condition” and study the existence and uniqueness of solution for a general class of abstract differential equations with state dependent delay subject to this class of conditions. In this type of problem the nonlocal condition can be dependent on times or time intervals determined by the (unknown) solution. Some examples on partial differential equations with state dependent delay arising in population dynamics are presented.