Asymptotic Behavior of Rupture Solutions for the Elliptic MEMS Equation with H\'enon-Type and External Pressure Terms
Abstract
This paper investigates an elliptic MEMS-Type equation with Henon and external pressure terms: Delta u = lambda|x|alpha / up + F for x in RN \ 0, with u(0)=0 and u>0 for x in RN \ 0, where N >= 1, lambda > 0, p > 0, alpha > -2 and F in R are constants. We study positive rupture solutions with rupture point at the origin (u(0)=0). Our main emphasis is on asymptotic radial rupture solutions: we prove the existence of both radial and non-radial solutions, characterize their asymptotic behavior near the origin, and obtain a full asymptotic expansion of arbitrary order.
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