We investigate existence, multiplicity and qualitative properties of the solutions of the Dirichlet problem for the singularly perturbed prescribed mean curvature equation $\left\{\begin{array}{cc}\hfill -(1-bu)\mathrm{div}\left(\frac{\nabla u}{\sqrt{1+{|\nabla u|}^2}}\right)=\frac{a}{{(u-R)}^2}+\frac{b}{\sqrt{1+{|\nabla u|}^2}},\hfill & \text{in}\Omega ,\hfill \\ \hfill u=0,\hfill & \text{on}\partial \Omega ,\hfill \end{array}\right.$where $a,b,R$ are given constants and $\Omega$ is a bounded regular domain in ${\mathbb{R}}^N$. This model appears in the theory of micro-electro-mechanical systems (MEMS) when the effects of capillarity and vertical forces are taken into account.

中文翻译：

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曲率方程建模的垂直载荷微机电系统的定性分析

我们研究奇摄动的平均曲率方程Dirichlet问题解的存在性，多重性和定性性质 $\left\{\begin{array}{cc}\hfill -（\mathrm{1个}-bü）\mathrm{div}（\frac{\nabla ü}{\sqrt{\mathrm{1个}+{|\nabla ü|}^2}}）=\frac{\mathrm{一种}}{{（ü-\mathrm{[R}）}^2}+\frac{b}{\sqrt{\mathrm{1个}+{|\nabla ü|}^2}}，\hfill & \text{在}\Omega ，\hfill \\ \hfill ü=0，\hfill & \text{上}\partial \Omega ，\hfill \end{array}\right.$哪里 $\mathrm{一种}，b，\mathrm{[R}$ 被赋予常数和 $\Omega$ 是位于 ${\mathbb{[R}}^{ñ}$。考虑到毛细作用和垂直力的影响，该模型出现在微机电系统（MEMS）理论中。