Use the range
type. If the user enter a date:
select *
from table
where
update_date
<@
tsrange('2013-05-03', '2013-05-03'::date + 1, '[)');
If the user enters timestamps then you don't need the ::date + 1
part
http://www.postgresql.org/docs/9.2/static/rangetypes.html
http://www.postgresql.org/docs/9.2/static/functions-range.html