My table myTab has the column startDate, which has the datatype \"DATE\". The data in this column are stored like dd.mm.yyyy.
myTab
startDate
dd.mm.yyyy
Regarding you actual question "Somehow it doesn't work and I don't know why."
Oracle make an implicit conversion from DATE to VARHCAR2, however it uses the default NLS_DATE_FORMAT which is probably different to what you use in your query.
DATE
VARHCAR2
NLS_DATE_FORMAT