Assuming the DATE from user interface can contain times besides 00:00:00 (midnight) and that you only want to know if the DATE from the user interface and the TIMESTAMP fall on the same day (not same hour or minute or ?), try this:
-- Change TIMESTAMP to a DATE type with CAST, then TRUNCate time to 00:00:00.
myDatabaseDate := TRUNC( CAST(myDatabaseTimeStamp as DATE) );
myDatabaseNextDay := myDatabaseDate + 1;
SELECT something into some_var
WHERE inputDate < myDatabaseNextDay
AND inputDate >= myDatabaseDate;
Note 1: Because "inputDate" is a database column and could be indexed, we don't want to do
TRUNC(inputDate) because then the index won't be used.
Note 2: Doing the CAST before the SQL statement prevents this PL/SQL compilation warning: PLW-07204: conversion away from column type may result in sub-optimal query plan ... Edit: After testing this on 10.2 XE, even the "myDatabaseDate + 1" causes the warning so, although it seems like doing too much to please the compiler, I added "myDatabaseNextDay := myDatabaseDate + 1;"