If you want a cheap flight from Linz to Rome, you've got zero airlines to choose from.
You can use the filters on your search to see more flights and find cheaper rates – Rome has more than one airport. So if you don't need to fly into Rome Leonardo da Vinci International (Fiumicino) Airport, it's worth checking your other options.
If you're planning on going to Rome during this time, you could take a look at other airport options. Or you could try to get a last-minute bargain.