A valve system controls flow into a downhole production string, and which includes a downhole valve with a port formed in a sidewall of a production string disposed in a wellbore, and a sleeve that is slidable along the production string to block or allow flow through the port. An actuator assembly exerts a sliding force onto the sleeve, and is made up of multiple actuators arranged along an outer surface of the production string. Each actuator has an electrically powered motor and a stem connected to the motor. An opposite end of each stem connects to an end of the sleeve. Energizing the motors causes linear movement of the stems and connected sleeve to open and close the valve.