How to find rows that have a value that contains a lowercase letter

I'm looking for an SQL query that gives me all rows where ColumnX contains any lowercase letter (e.g. "1234aaaa5789"). Same for uppercase.

SELECT * FROM my_table 
WHERE UPPER(some_field) != some_field

This should work with funny characters like åäöøüæï. You might need to use a language-specific utf-8 collation for the table.

SELECT * FROM my_table WHERE my_column = 'my string'
COLLATE Latin1_General_CS_AS

This would make a case sensitive search.

EDIT

As stated in kouton's comment here and tormuto's comment here whosoever faces problem with the below collation

COLLATE Latin1_General_CS_AS

should first check the default collation for their SQL server, their respective database and the column in question; and pass in the default collation with the query expression. List of collations can be found here.

SELECT * FROM Yourtable 
WHERE UPPER([column_NAME]) COLLATE Latin1_General_CS_AS !=[Column_NAME]