Despite comments by SCEE President, David Rees, indicating that Sony is not planning a PSP successor at the moment, word from Eurogamer is that various "publishing sources" know better. According to those sources, both an iterative successor to the current PSP and a successor are well under development.
Apparently late next year will see yet another tweaked PSP released, in the styles of the PSP-3000 update, perhaps fixing those screen problems. Eurogamer's sources were unable or unwilling to give even a timescale on the PSP2 (assuming that's what it will be called), but would confirm that games are already under production ready for the platform.
Admittedly Rees never denied that such development was taking pace, merely commenting: "I go to Tokyo quite a lot and no one has referred to it - I think they have their hands full at the moment." It's hardly surprising to hear Sony is working on a successor to the PSP, which has been out for some five years now but, hey, confirmation is always good.