Summary: We study the exact controllability of the following semilinear difference equation
, , where , are Hilbert spaces, , , , and the nonlinear term satisfies:
We prove the following statement: If the linear equation is exactly controllable and , then the nonlinear equation is also exactly controllable. That it to say, the controllability of the linear equation is preserved under nonlinear perturbation . Finally, we apply this result to a discrete version of the semilinear heat equation.