Singular Behavior of an Electrostatic--Elastic Membrane System with an External Pressure

Yujin Guo, Yanyan Zhang, Feng Zhou

We analyze nonnegative solutions of the nonlinear elliptic problem $\Delta u=\frac{\lambda f(x)}{u^2}+P$, where $\lambda >0$ and $P\ge 0$, on a bounded domain $\Omega$ of ${\mathbb{R}}^N$ ($N\ge 1$) with a…