Exact multiplicity results for a one-dimensional prescribed mean curvature problem related to MEMS models

In this paper, we consider a one-dimensional prescribed mean curvature problem related to MEMS models. We obtain all exact multiplicity for classical solutions and non-classical solutions when the length LL of the interval and the parameter λλ change. As a by-product, it also provides a complete analytic proof for an interesting new phenomenon, which is first noticed by Brubaker and Pelesko. Our methods are based on a detailed analysis of time maps.