We investigate radial solutions for the problem \[ \begin{ cases} \displaystyle -\Delta U=\frac{ \lambda+\delta|\nabla U|^2}{ 1-U},\; U>0 & \textrm{ in}\ B,\\ U=0 & \textrm{ on}\ \partial B, \end{ cases} \] which is related to the study of Micro-Electromechanical Systems (MEMS). Here, $B\subset \mathbb{ R}^N$ $(N\geq 2)$ denotes the open unit ball and $\lambda, \delta>0$ are real numbers. Two classes of solutions are considered in this work: (i) { \it regular solutions}, which satisfy $0<U<1$ in $B$ and (ii) { \it rupture solutions} which satisfy $U(0)=1$, and thus make the equation singular at the origin. Bifurcation with respect to parameter $\lambda>0$ is also discussed.
Categories: math.AP