A perturbed fourth order elliptic equation with negative exponent

Zongming Guo; Long Wei

doi:10.3934/dcdsb.2018132

Article Contents

2018, Volume 23, Issue 10: 4187-4205. Doi: 10.3934/dcdsb.2018132

This issue Previous Article On the Cauchy problem for the XFEL Schrödinger equation Next Article Carleman estimate for solutions to a degenerate convection-diffusion equation

A perturbed fourth order elliptic equation with negative exponent

Zongming Guo^1, and
Long Wei^2, ,

1.
Department of Mathematics, Henan Normal University, Xinxiang 453007, China
2.
Department of Mathematics, Hangzhou Dianzi University, Zhejiang 310018, China

* Corresponding author
* Corresponding author

Received: July 31, 2017

Revised: November 30, 2017

Early access: April 2018

Published: September 2018

The research of the first author is supported by NSFC (11571093).

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Abstract

By a new type of comparison principle for a fourth order elliptic problem in general domains, we investigate the structure of positive solutions to Navier boundary value problems of a perturbed fourth order elliptic equation with negative exponent, which arises in the study of the deflection of charged plates in electrostatic actuators in the modeling of electrostatic micro-electromechanical systems (MEMS). It is seen that the structure of solutions relies on the boundary values. The global branches of solutions to the Navier boundary value problems are established. We also show that the behaviors of these branches are relatively "stable" with respect to the Navier boundary values.

Keywords:

Perturbed fourth order elliptic equations,
Navier boundary value problems,
negative exponent,
branches of solutions.

Mathematics Subject Classification: Primary: 35B45; Secondary: 35J40.

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