How on earth do I install kitchen cabinets in a round log kitchen without them eventually skewing from settling???
One way is to route a groove into the wall to accept a 2 x 4, just like you would with a partition wall. The 2 x 4 needs to be screwed down tight at either the top or the bottom, then slot the 2 x for the rest of the screws into the logs. Of course, the screws in the slots will just want the head touching, not tight.
Mount the cabinets to the 2x. You probably could even get by with a 1 x. Use however many 2x's or 1 x's you need to make a stable mounting. If the cabinets are fastened together tight at the front and back, it makes them more like a unit, and you won't need a vertical support on each one.
You can try installing Ready to assemble kitchen cabinets.
If anyone comes up against any problems like this, I recommend contacting https://walcraftcabinetry.com to help. They can help you with designing and creating any kitchen cabinet space that would work in any situation. Even round ones!