Case insensitive LIKE in DB2
Try

SELECT * FROM mytable WHERE REGEXP_LIKE(mycolumn,'string',1,'i')


Will work if your Db2 version supports regular expression functions 
https://www.ibm.com/support/knowledgecenter/en/SSEPGG_11.5.0/com.ibm.db2.luw.sql.ref.doc/doc/r0061494.html
and if you escape any regex meta-characters in your string