Hi Alex,
i have no clue about PowerBuilder, but i can answer your question from an Oracle perspective of course.
> Can a PowerBuilder application log into an Oracle database, which uses an LDAP server.
What do you mean with "log into"? SQL*Net name resolution, authentication or what? You can use OID or AD as a LDAP server (Parameter DIRECTORY_SERVER_TYPE)
Oracle Documentation: http://docs.oracle.com/cd/E11882_01/network.112/e10835/ldap.htm#NETRF362
You can use Kerberos for user authentication, if you have licensed the Oracle Advanced Security option:
http://docs.oracle.com/cd/E11882_01/network.112/e10746/asokerb.htm#ASOAG060
> Probably about an OS authentication or something else?
This depends on your Oracle version and configuration. Remote OS authentication is deprecated, but still possible in Oracle 11g. But i would not build up new applications on that authentication mechanism as it is retained for backward compatibility only.
Oracle Documentation: http://docs.oracle.com/cd/E11882_01/server.112/e25513/initparams211.htm#REFRN10185
Regards
Stefan