According to your link here.... If we stop at Crush, Desmond only co-wrote 7 "major hits" with Jon and Richie and I question a few of these as "major" hits but yet my list, that stopped around Crush, included 12 songs that were written with just Jon and Richie.

But to be honest, this is old news to me so unless you find some earth shattering article that discredits any of this, you are just coming off like a novice Bon Jovi fan to me. Sorry dude! Happy Holidays!

"You Give Love a Bad Name"
"Livin' on a Prayer"
"Bad Medicine"
"Born to Be My Baby"
"Keep the Faith"
"Something for the Pain"
"This Ain't a Love Song"