What was found
ON DEPARTURE WHILE SELECTING THE GEAR UP WE RECEIVED STEERING INOP (C) MSG. FOLLOWING THAT MSG WE GOT A GEAR DISAGREE (W) MSG AND A NOSE DOOR (W) MSG. NOSE DOOR (W) MSG WENT AWAY ON ITS OWN. NOSE GEAR WAS SHOWING DOWN ON EICAS WHEN THE HANDLE WAS IN THE UP POSITION. COMPLIED WITH QRH AND IT CLEARED THE MSG AND THE GEAR WENT UP. AFTER COMPLETING QRH, PERFORMED THE QRH FOR STEERING INOP AND IT CLEARED THE STEERING MSG. NO FURTHER ISSUES AFTER BOTH QRH WAS C/W. DID NOT LAND OVERWEIGHTDID NOT DECLARE EMERGENCY (FLIGHT 5375 FILED OPEN)