ABSTRACT

In this paper we consider a class of one-dimensional optimal control problems of the state equation of delay type, namely, a state equation of the form (we call y the state variable and γ the control):

 y(t) =

∫ 0 −T γ(t+ s)ς(s)ds

γ(s) = ι¯(s) ∀s ∈ [−T, 0) y(0) =

where ς : [−T, 0] → R+ is a positive BV-function and ι¯ ∈ L2((−T, 0); R+) (with y(0), which is determined by ι¯) is the initial datum that in the delay setting involve the history of the variables.