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Evading fixed point theorems we prove the interior approximate controllability of the following semilinear strongly damped wave equation with impulses and delay    in the space Z 1/2  = D((−Δ) 1/2 )×L 2 (Ω),where r &gt; 0 is the delay, Γ = (0, τ)×Ω, ∂Γ = (0, τ) × ∂Ω, Γ r  = [−r, 0] × Ω, (ϕ,ψ) ∈ C([−r, 0]; Z 1/2 ), k = 1, 2, . . . , p, Ω is a bounded domain in ℝ ℕ (ℕ ≥ 1), ω is an open nonempty subset of , 1 ω denotes the characteristic function of the set ω, the distributed control u ∈ L 2 (0, τ; U), with U = L 2 (Ω),η,γ, are positive numbers and f , I k  ∈ C([0, τ] × ℝ × ℝ; ℝ), k = 1, 2, 3, . . . , p. Under some conditions we prove the following statement: For all open nonempty subsets Ω of the system is approximately controllable on [0,τ]. Moreover, we exhibit a sequence of controls steering the nonlinear system from an initial state (ϕ (0), ψ(0)) to an ε-neighborhood of the final state z 1  at time τ &gt; 0.

Controllability of the Strongly Damped Wave Equation with Impulses and Delay