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arXiv · 2512.05743

Asymptotic Behavior of Rupture Solutions for the Elliptic MEMS Equation with H\'enon-Type and External Pressure Terms

Yunxiao Li·Yanyan Zhang
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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.

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Yunxiao Li, Yanyan Zhang. 2025-12-05. Asymptotic Behavior of Rupture Solutions for the Elliptic MEMS Equation with H\'enon-Type and External Pressure Terms. https://arxiv.org/abs/2512.05743

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