Sandra,
You say this is Java. Is an application server used? If so, the application server connection settings may have some effect.
Modern O-O applications like this do indeed consume a staggering number of open cursors. That is just the way it is -- increase OPEN_CURSORS and move to the next issue.
I have not seen any effect on the database. I suspect the additional cursors probably consumes some additional memory, but I have no facts.