Abstract
We investigate existence, multiplicity and qualitative properties of the solutions of the Dirichlet problem for the singularly perturbed prescribed mean curvature equation −(1−bu)div(∇u1+|∇u|2)=a(u−R)2+b1+|∇u|2,inΩ,u=0,on∂Ω,where a,b,R are given constants and Ω is a bounded regular domain in RN. This model appears in the theory of micro-electro-mechanical systems (MEMS) when the effects of capillarity and vertical forces are taken into account.
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