Ceiling wall paper coming off at edges

If it is Anaglypta type paper, then mix up some normal wall paper paste. Use a childs paint brush to get it inside the joints. Wait 5-10 mins for paper to soften and smooth down

Patterned Paper, I use a paper glue stick ("Pritt" etc.)

 

Just leave it soak for a while and then smooth it down with a tea towel or similar

 

If it is only here and there you can use decorators caulk. After application push into place and remove the excess with a damp sponge/rag.