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We consider a parabolic problem with Robin boundary condition which ariseswhen the edge of a micro-electro-mechanical-system (MEMS) device is connectedwith a flexible nonideal support. Then via a rigorous analysis we investigatethe structure of the solution set of the corresponding steady-state problem. Weshow that a critical value (the pull-in voltage) exists so that the system hasexactly two stationary solutions when the applied voltage is lower than thiscritical value, one stationary solution for applying this critical voltage, andno stationary solution above the critical voltage.

Bifurcation diagram of a Robin boundary value problem arising in MEMS