“…Example The original Benjamin–Bona–Mohany Equation is a non‐linear one, in [] the authors proved the approximate controllability of the linear part of this equation, which is the fundamental base for the study of the controllability of the non linear BBM equation, which in fact, was studied in []. So, our next work is concerned with the controllability of the impulsive non linear BBM equation with delay in control and in state where 0 ≤ r 1 ≤ r < τ , a ≥ 0 and b > 0 are constants, Ω is a domain in I R N , ω is an open nonempty subset of Ω, 1 ω denotes the characteristic function of the set ω , the distributed control u ∈ L 2 (0, τ ; L 2 (Ω)), ϕ :[ − r ,0] × Ω→ I R is a continuous function and f ( t , z , u ) is a nonlinear perturbation.…”