The only way that I am aware of is in-app purchasing. This is similar to the old 80's or 90's business model of releasing Demo versions that work but don't expose all of the possible functionality.
So there's two ways to go:
1) Release a free and a non-free version of the app. Some users will like the free version and buy the paid one.
2) Release only a free version of the app, but use in-app purchases to unlock features.
Either way you will want to spam them about the paid upgrades once in a while.