Abstract
We first recall how the classical Melan equation for suspension bridges is derived. We discuss the origin of its nonlinearity and the possible forms of the nonlocal term: we show that some alternative forms may lead to fairly different responses. Then we prove several existence results through fixed point theorems applied to suitable maps. The problem appears to be ill-posed: we exhibit a counterexample to uniqueness. Finally, we implement a numerical procedure in order to try to approximate the solution; it turns out that the fixed point may be quite unstable for actual suspension bridges. Several open problems are suggested.