Hi! I'm seeking some help for my problem. Please don't mind my bad english

My problem is that every time I start the car, it starts just fine and runs fine for about 10 seconds. After that it sutters and dies. After second start it usually runs and doesn't die. Where do I start looking for solution?
I also experience slight lack of power between 3500-4000rpm, after that it accelerates normally.. Could these problems be related? Something fuel related?