What, exactly, is the problem?
Normally, the middle tier application server creates a connection pool. When your code requests a connection, it gets an already open connection from the pool rather than going through the overhead of spawning a new connection to the database. When your code closes a connection, the connection is returned to the pool rather than going through the overhead of physically closing the connection. That means that there will be a reasonable number of connections to the database where the
V$SESSION is "INACTIVE" at any given point in time. That's perfectly normal.
Even under load, most database connections from a middle tier are "INACTIVE" most of the time. A status of "INACTIVE" merely means that at the instant you ran the query, the session was not executing a SQL statement. Most connections will spend most of their time either sitting in the connection pool waiting for a Java session to open them or waiting on the Java session to do something with the data or waiting on the network to transfer data between the machines.
Are you actually getting an error (i.e. ORA-00020: maximum number of processes exceeded)? Or are you just confused by the number of entries in