Is there any way White can win this?

I was playing as white against the computer.  Black played the Sicilian and after a few blunders I found myself in this position.  I ended up losing, after Qg5?, but was wondering if there was any way to win.

I considered resigning because after:

1. Qc4, but had no answer for Rc8 except Nc7, which didn't help.

1. Nc7 Rc8, the Knight falls any way

1. Qc7 Qxb5

The best I seemed to be able to do was to trade that Knight for a Pawn.

I considered 1. Nxe5, attacking the Queen and making the trade right away

I decided on 1. Qg5 because I could trade the knight for the two center black pawns and try to gain the iniative.

The thinking was after 1....Qxb5, 2. Nxd4 Qd7 3. Qxd4  (winning two pawns for the knight)

But after 3....Bd6, I couldn't find a suitable answer

I think you're in good shape after 1. Qc4 Rc8  2. Qd3 Bd6 (the only way to guard the e5 pawn) 3. Nxd6 Qxd6  4. Qb5 attacking the b7 and e5 pawns. If he tries to get counterplay with 4 ... d3 then 5 Rd1 Ne4  6. Rd3 gives you an advantage due to your better pawn structure.

This is very helpful, Splane.  I was wondering how I could exploit black's pawn structure, but I couldn't see it.  I typically try to attack too soon in these types of positions.  Thanks

@BorQueen and @RoseQueen1985:

Thanks for your comments