Question: Are there adult videos on PSP UMD?
Answer: Yes, in fact, though you won't find them listed on the English Wikipedia. X-rated UMD videos are almost exclusively from Asia (UMD Region 2). Although they were not released in the North American territories, it is possible to import these videos and view them on domestic PSP systems with some firmware hacks. (Of course, they will also play on Asian-region PSPs without modification.)
You can find several Adult UMD videos being sold by import retailers like Play-Asia.com, though they are largely out of stock these days. Anyone can anonymously browse the list of these videos. If your child has bought a foreign PSP bundle, or has a hacked PSP, be sure to know whether they're also buying adult UMD videos. As always, try to be an active participant in your child's online transactions, even if that means just asking what PSP games or videos they have been looking at lately.