When I connect my raspberry pi to a monitor through an HDMI cable, the resolution gets lower at the boot of the desktop UI, but when I click on start menu it turns to 1920×1080. Sometimes it randomly changes. I set the resolution at 1920×1080. What is the matter?
Unless this is the result of some prior fiddling with the resolution, I'd say that either your HDMI cable, your monitor or your Raspberry Pi is broken. Try another cable, or another monitor first. Or flash a fresh Raspbian onto another SD card and boot from that. Any changes?