Permit the user to define the search. E.g. choose between blank, not blank, greater than, etc.
Ruth Allen commented
You can define searches for all of the options you mentioned. Create a drop-down of search options and define the value of blank, not blank and greater than, etc. or you can create multiple search option fields and define the form elements separately for those options. For the greater than option, you may need to have a numeric field type.