Q: Downloaded books in itunes but doesn't show on iphone

When the iPhone is connected to iTunes, go to the Books tab (top right) and check Sync books.

Are you using the same Apple ID on your iPhone, iPad, and computer (iTunes)?  Are you relying on iCloud to sync bookmarks, etc.?

OK, then go to Settings > iTunes & App Stores on your iPhone and make sure books is set to "On" and your Apple ID is set correctly at the top.

Here's a good reference article on the subject:

http://support.apple.com/kb/HT4539

I hope something mentioned there will trigger success.