OPEN_CURSORS instance wide vs. per session

We had the problem that we ran out of max open cursors with an instance. After increasing the number by using

alter system set open_cursors=1000 scope=both;

it worked (for a while). Now we again have a problem at the customer's site. I don't have a definite

error message yet, but may I ask here already a question:

Instance wide is the number of cursors set to 1000 with the above command.

Does this apply to any session/process?

I was using this to to obtain a picture. Would that be appropriate to analyze the problem?

SQL> select count(*) from v$open_cursor;

  COUNT(*)
----------
       572

SQL> select max(a.value) as highest_open_cur, p.value as max_open_cur
  2    from v$sesstat a, v$statname b, v$parameter p
  3    where a.statistic# = b.statistic#
  4    and b.name = 'opened cursors current'
  5    and p.name= 'open_cursors'
  6    group by p.value;

HIGHEST_OPEN_CUR
----------------
MAX_OPEN_CUR
--------------------------------------------------------------------------------

              47
1000