We study the branch of semi-stable and unstable solutions (i.e., those whose Morse index is at most one) of the Dirichlet boundary value problem −∆u = λf(x) (1−u)2 on a bounded domain Ω ⊂ R , which models –among other things– a simple electrostatic Micro-Electromechanical System (MEMS) device. We extend the results of [11] relating to the minimal branch, by… (More)