There are numerous opinions in the Gemara, in Maseches P’sachim, as to who authored these chapters of T’hilim (113-118), which comprise what we refer to as “Hallel.” It has been suggested that there is really no dispute in the Gemara. The basic framework was established by the early Prophets and later enhanced by successive generations. Eventually, David HaMelech organized these chapters into the final form we have today in T’hilim (T’shuvah MeiAhavah, Vol. II, responsum 264).