Hell is living without you was written by Alice, Jon, Richie and Desmond Child. Desmond co-wrote all the songs on "Trash".
And I just found out by reading the booklet for the first time(12 years after I bought that CD) that there is a line that says: "Richie Sambora, Steve Lukather: additional guitar on "Hell is living without you". Wow, didn't know that. Huey played bass on the album by the way. And Jon sings additional vocals on "Trash" (the song not the album) but at least I knew that already.