My wife really wants an over-the-range microwave. However, our range is set on a diagonal (45 degrees) relative to the wall and counter, meaning the microwave would be at an angle relative to the studs in the wall.
There's a cabinet above, and a range hood hung there previously, so there's plenty of upper surface. There's also about a 3" cabinet back (made out of particle board or similar) where the range hood used to be, so the upper portion of the microwave could be affixed to something if necessary. However, there's not even drywall behind where the microwave would go, let alone a stud, and no good way to get anything in there without closing off a bunch of countertop space, which would defeat the purpose of having an over-the-range microwave.
I know someone here knows how to hang a microwave without a back wall - teach me your ways!