Asymptotic Behavior of Rupture Solutions for the Elliptic MEMS Equation with Hénon-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 / u^p + F for x in R^N \ {0}, with u(0)=0 and u>0 for x in R^N \ {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.

47 pages, 1 figure. This version contains additional improvements and refinements of the previous manuscript. The author list has also been updated to include Prof. Yanyan Zhang, who contributed to the development of this work