I will try:
select to_date(given_date) from your_table
where to_date(given_date,'mm/dd/yyyy') < to_char(sysdate,'mm/dd/yyyy')
or to_date(given_date,'mm/dd/yyyy') = to_char(sysdate,'mm/dd/yyyy')
or to_date(given_date,'mm/dd/yyyy') > to_char(sysdate,'mm/dd/yyyy');
or you can test them individually by testing for:
to_date(given_date,'mm/dd/yyyy') < to_char(sysdate,'mm/dd/yyyy') first
and to_date(given_date,'mm/dd/yyyy') = to_char(sysdate,'mm/dd/yyyy') second
or to_date(given_date,'mm/dd/yyyy') > to_char(sysdate,'mm/dd/yyyy') third
or any combination.