I have this issue with the UP2414Q monitor and my new Mac Pro . . . . . and then some.
I started by losing the right half of the screen on wake up. After about two months of use, my monitor has developed a fault where both sides of the monitor are displayed but at seemingly very different calibrations. The left half is contrasty and the right half seems to be correctly matched to my working profile. This is using the display port connections. HDMI doesn't have this problem but it also won't run at 60Hz, which was an important factor in my choice of this monitor.
At this point I contacted both Apple and Dell. Although I have had quite a few different Apple support staff over a period of a week or so, they did keep good notes, were very patent and seemed to take a genuine interest into trouble shooting it. I cannot say the same for Dell. At first they did ask questions and did the right thing by sending a replacement. It worked fine on display port, then on HDMI but when I connected it back to display port the split screen problem occurred on the brand new replacement one too. After a day of fiddling with connections it went back to displaying correctly with all connections and has not reverted but it does now have the dead right halve on wakeup more frequently than before. I reconnected the original monitor but that has the split screen problem and I can't find a way of getting it to go away. It is unusable.
This incident with the replacement monitor was five days ago. In that time I have tried to contact Dell support by the original e-mail of the technician that initially helped and by phone, through the support number. The email gets the repeated response "Dear Sir/Madam, Thank you for your email. I have left for the day, hence my reply will be delay". It happens in the mooring or the afternoon. A phone call to Dell's support number always starts with a promise to be transferred to the technician dealing with my case and, without fail ends by me being left on hold indefinitely with a terrible one minute audio loop followed by a repeated promise of the next available agent. I once waited over 30 minutes, just to test it. I live in Australia but this was clearly an international call centre. Dell obviously have no intention of dealing with my case. They will have to talk soon though because I still have an extra one of their monitors.
Unless there is a firmware update for this monitor, I would strongly advise against buying one for a Mac, or any Dell product for that matter.