Radial single point rupture solutions for a general MEMS model

We study the initial value problem {r(-(gamma-1)) (r(alpha) vertical bar u'vertical bar(beta-1)u')' = 1/f(u) for 0 < r < r(0), u(r) > 0 for 0 < r < r(0,) u(0) = 0, for gamma > alpha > beta >= 1 and f is an element of C[0, (u) over bar)boolean AND C-2 (0, (u) over bar), f(0) = 0, f(u) > 0 on (0, (u) over bar) and f satisfies certain assumptions which include the standard case of pure power nonlinearities encountered in the study of Micro-Electromechanical Systems (MF,MS). We obtain the existence and uniqueness of a solution u* to the above problem, the rate at which it approaches the value zero at the origin and the intersection number of points with the corresponding regular solutions u (center dot , a) (with u (0, a) = a) as a -> 0. In particular, these results yield the uniqueness of a radial single point rupture solution and other qualitative properties for MEMS models. The bifurcation diagram is also investigated.