I am running HP-UX 11.31 ia64. The /usr filesystem shows 7 GB as the size, but the logical volume that is mounted there shows 13 GB. Is there a way to get the entire 13 GB to show up and why did this happen in the first place?

Can you explain how you got those figures?

The df -k of /usr shows 7143528 Kbytes but when I run a lvdisplay for /usr, it shows 13312 Mbytes.

Since you have not produced the output of the exact commands you passed, lets do things differently:
Q - What Do I do once I created a FS in order to use it
A - Create a FS...
Q - should it occupy all the LV?
A - Not necessarily...
Q - I create a FS that occupy the half of the LV fo I am a bit paranoid...Now I want to incease a bit its size, How can it be done?
A - Either you have Online-JFS, it can be done on the fly using fsadm, or look at the man pages of extendfs

Sorry for not posting my results. I'm new to forums.

If I read the man page correctly, I must first unmount the FS. Since this is the OS, I'm assuming I have to be in single user mode since the FS is in use?
If these statements are true, I will try that first before taking any more of your time and either close this thread or reply with my results.
Thanks.

Do you know if you have Online-JFS installed?

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addendum:

ant:/home/vbe $ swlist -l product|grep JFS
  JFS                   B.11.11        The Base VxFS File System 
  OnlineJFS             B.11.11.03.03  Online features of the VxFS File System 
  PHKL_24026            1.0            JFS Filesystem swap corruption 
  PHKL_28512            1.0            Fix for POSIX_AIO in JFS3.3 
  PHKL_29115            1.0            JFS Direct I/O cumulative patch 
  PHKL_30366            1.0            JFS3.3;ACL patch 
  PHKL_34805            1.0            JFS3.3 patch; mmap 
  PHKL_35329            1.0            JFS3.3 edquota performance improvement 
  PHKL_35933            1.0            Panic extending JFS3.3 filesystem past 128GB

If you want my point of vue, it looks like someone extended the lvol thinking the FS would follow... not true by command line but if you were to use SAM it would have extended the filesystem also...