Is there a way that I can sync PDF files on Mendeley with the iBooks app on the iPhone. As an alternative is there a way I can sync the files with any PDF reader on the iPhone?
If you can download those PDFs to your computer, just drag them into your iTunes library. The "Books" subsection will be created (if it isn't already) next to Music, Movies, Podcasts, Apps, etc. and then you can sync them to your iPhone quite easily.