SQLite select-string with umlaut

Here's a simple problem but I can't solve it alone since I'm not really familiar with SQL.

Most of you may already know this, in German there are umlaut-letters, e.g. "Ä,Ö,Ü", the lower case of them would be "ä,ö,ü".

I'm using a sqlite-database, accessing it with the Firefox plugin "SQLiteManager". My select string looks like this:

SELECT * FROM Projects WHERE Token LIKE '%ä%'

The Firefox plugin and also a SQLite library for .NET both return the wrong output. They return not only the entries with the lower case "ä", but also the entries with the upper case "Ä".

Do you guys know a simple solution to this? Thanks in advance!