I'm sure Muhammad existed...there is quite a legacy of death in his name as well as a fair amount of written evidence of his life.
Muslims claim he wasn't literate, and therefore, the Quran was written down in various bits over a many year period of time. There are more than 1 version of the Quran, contrary to Muslim claims to the contrary, and there are also issues, such as the "Satanic Verses" made famous in the West by Salman Rushdie. The essence of those is Muhammad thought he was possessed by Satan. One can imagine why that wouldn't be a popular bit to leave in the Quran.