Originally Posted by
meganova
There is one application that can convert PSN Eboots into ISO, however the chances it will work after conversion is pretty slim, especially if you try to run it on JPCSP.
The application is called EBOOT2ISO(google for it), and you won't get an ISO file after converting it, but instead a folder with set of files that need to be compiled using UMDGen, then finally it will be saved as an ISO.
PSX games can't be run on JPCSP, as it whole purpose is to load PSP backups, so you need to use ePSXe for that.
I'm not sure what format does PS1 Classic from PSN comes with, but if its in Eboots, try using the above method and hope it will work.