Abstract
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 L of the interval and the parameter λ 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.
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