I've tried several different was all being unsuccessful.   Someone continues to create new accounts and send messages to my girlfriend and I.  I know it is the same person due to the crap profile they create.  I can block them but a day later a similar message appears from a similar crap profile. Any way to block messages from non friends or any other way to put an end to this?

tell facebook.  they can get to the ip of the person and deal with it

Find the person and set them on fire? 

Send them a care package of Africanized bees? 

I think you should share with the class why you and your GF have earned this individual's ire. 

Uninstall Facebook, Facebook messenger, and be done with it.

Have you tried setting your account profile to private and making sure your posts are viewable to friends only?

I've looked for a contact via email.and can't locate one.

Yes.  Didn't help.

I had the same problem

Can't you report it as spam? I thought that was an option when somebody not on your friend list sent you a message.

What did you do to resolve the issue?

Unfortunately Facebook in all of its infinite wisdom decided to make it impossible to hide from people basically. You used to be able to hide your profile completely and only be able to be found by your email address you used to sign up IF you had it set that way, if not then the only time your profile was seen was either by people you are already friends with, or people you have just sent a friend request to.

If you know the person doing it, call the local law enforcements. If not wait till the next time they do it, then get in contact with facebook support asap, give them your story, give them a link to the current fake profile, and really dig to get them to IP ban any and all IP addresses associated with that account.

Hopefully the little shit isn't smart enough to be changing IP addresses.

Edit: FACEBOOK IN ALL OF THEIR INFINITE WISDOM DOES NOT EVEN HAVE A WAY TO CONTACT THEM OTHER THEN REPORTING BASICALLY....GG Facebook...either just keep reporting the fake profile and then block it....or contact law enforcement. Or better yet do as stated above and get off facebook completely.