How to find substring inside a string (or how to grep a variable)?

I'm using BASH, and I don't know how to find a substring. It keeps failing, I've got a string (should this be an array?)

Below, LIST is a string list of database names, SOURCE is the reply, one of those databases. The following still doesn't work:

echo "******************************************************************"
echo "*                  DB2 Offline Backup Script                     *"
echo "******************************************************************"
echo "What's the name of of the  database you would like to backup?"
echo "It will be named one in this list:"
echo ""
LIST=`db2 list database directory | grep "Database alias" | awk '{print $4}'`
echo $LIST
echo ""
echo "******************************************************************"
echo -n ">>> "
read -e SOURCE

if expr match "$LIST" "$SOURCE"; then
    echo "match"
    exit -1
else
    echo "no match"
fi
exit -1

I've also tried this but doesn't work:

if [ `expr match "$LIST" '$SOURCE'` ]; then