2003 Cadillac Deville acting crazy Will start and drive then I will comeback and nope
 

My 2003 Cadillac Deville will start right up and ride fine may idle here and there but not a lot but sometimes when I comeback to leave a store or something I will try to start it it will turn over but immediately cut off and if i keep my foot on the gas it will stay started up. It can sit for a few hours and it will statr back up like nothing has happened. What could the issue be.