I want free database will be able to ship with my commercial application. It shouldn't have installation (i.e., no window service with no setup).
It may be single user database. It will operate in Home windows atmosphere and used from Java code.
Consider SQLite. I've not tried on the extender, but I have had applications that stated for doing things, and that i could not differentiate.
What about SQLite? It's good performance, with one user it's not necessary to be worried about concurrency.
Oracle Berkeley DB: http://www.oracle.com/database/berkeley-db/index.html