AIX

Ok,
Close the other sessions if they are not required or least change the directory (say, go to default home directory of oracle). Nevertheless if you want to kill all the other sessions look below for fuser command
fuser -cuk /oragrid_01/Grid_11203, this will kill all the user sessions and open files used by user in the directory.

Make sure you run the above command from a different directory (as root and not as oracle).
Run df -g, if you still see the space occupied unmount/mount the filesystem it should resolve the problem.

The * in the du arguments won't show hidden files and directories, add .* to the arguments.
At least there will be the OPatch hidden storage directory.
Edit: I've just read that the application processes are down for maintenance.

Code:

 du -sg .*
52.89   .
53.58   ..
39.64   .patch_storage

Does this mean that .patch_storage occupies 39 GB and does this increase every time when we attempt applying the patch even in an unsuccessful attempt?

Yes, it does.
This is due to a bug on AIX. Check the following MOS note
FAQ: OPatch/Patch Questions/Issues for Oracle Clusterware (Grid Infrastructure or CRS) and RAC Environments (Doc ID 1339140.1)
search for: OPatch reports: "Prerequisite check CheckSystemSpace failed".

Thanks!

This doc helped me in resolving the issue



Best regards,
Vishal

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edit by bakunin: changed thread status to SOLVED