In the introduction to the novel, Niven says that he never planned to write more than one Ringworld novel, but that he did so, in a large part, due to fan support. Firstly, the popularity of Ringworld resulted in a demand for a sequel. Secondly, many fans had identified numerous engineering problems in the Ringworld as described in the novel. A major problem being that the Ringworld, being a rigid structure, was not actually in orbit around the star it encircled and would eventually drift, resulting in the entire structure colliding with its sun and disintegrating. In the novel's introduction, Niven says that MIT students attending the 1971 World Science Fiction Convention chanted, "The Ringworld is unstable! The Ringworld is unstable!" Niven says that one reason he wrote The Ringworld Engineers was to address these engineering problems.
Ringworld Prequel series (Larry Niven and Edward M. Lerner?)
Ringworld (Larry Niven)
More: The Ringworld