How do you beat a much stronger opponent?

Any tips? Suggestions? I'm very nervous about my middle game. My whole game falls apart there

Stronger? Just push. Give the game everything you've got. Block out every outside distraction and push yourself as hard as you possibly can. Once you reach a certain level of concentration, many moves will literally jump out at you. This, however, will not guarantee anything; if someone is stronger than that means your best may simply not be enough. But even a sharp knife will sometimes nick the hands of the master that wields it.

To play better then them :-)

My advice: Play to draw much stronger players, at least if you're playing Black.  If they give you winning chances you can always switch strategies and try to win, but if not I prefer to play it safe and I'm happy to draw a much stronger player when I can. 

I also like ViktorHNielsen's advice.

My advice: Ignore ratings. Just play your usual game, and try to beat them! Stronger players will not take risks, simply play untill you make a mistake. Just don't make mistakes, and they will get upset. I've drew 2 stronger players (+250 ELO) in a tournament, first time I played white, where I just played, waiting for him to make a mistake. He equalised and then he offered a draw in a superior position. I accepted.

Secondly, I tried to play safe. I got a bad endgame, where I played for 2 results. Lose or draw. I think he could sacrifice his bishop and get a strong passed pawn, but he didn't, and we just agreed to a draw after he had used 30 moves to try to crack my solid position.

What helps mentally is to know you've got nothing to lose, since it's the stronger player who has to justify his/her rating advantage, so pull no punches and play your favorite moves, trust your instincts, and if you lose the game, you still have something to review and learn from.  Only if you played your best ideas, can you improve upon them if you lose.  It's a win-win situation, as long as you give it your best.  Get in there and know you've already won.

Concentration and persistence...