Logon as system and execute the query:

select server, machine from v$session
where username = '';

if the server is NONE or SHARED you are using a shared server mode which means more connections to the database share the same server process, or if it is dedicated it means that every connection has it's owen server process.

If you are using JDBC OCI driver to connect to the DB put the cluase

(SERVER=DEDICATED)

in the tnsnames.ora file for the connection to the database For example:

DOGBERT2 =
(DESCRIPTION =
(ADDRESS = (PROTOCOL = TCP)(HOST = vip-rac1)(PORT = 1521))
(CONNECT_DATA =
(SERVER = DEDICATED)
(SERVICE_NAME = dogbert)
(INSTANCE_NAME = dogbert2)
)
)

This should make your connections dedicated (check with the above query that they really are). Then run the application again and see if the error persists.