Revisiting the Biharmonic equation modelling electrostatic actuation in lower dimensions

Zongming Guo; Baishun Lai; Dong Ye

doi:10.1090/S0002-9939-2014-11895-8

Revisiting the Biharmonic equation modelling electrostatic actuation in lower dimensions

Zongming Guo^*
, Baishun Lai
, Dong Ye

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

Let B ⊂ ℝ^N be the unit ball. We study the structure of solutions to the semilinear biharmonic problem [formula presented] where p, λ > 0, which arises in the study of the deflection of charged plates in electrostatic actuators. We study in particular the structure of solutions for N = 2 or 3 and show the existence of mountain-pass solutions under suitable conditions on p. Our results contribute to completing the picture of solutions in previous works. Moreover, we also analyze the asymptotic behavior of the constructed mountain-pass solutions as λ → 0.

Original language	English
Pages (from-to)	2027-2034
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	142
Issue number	6
DOIs	https://doi.org/10.1090/S0002-9939-2014-11895-8
State	Published - 1 Jun 2014
Externally published	Yes

Keywords

Asymptotic analysis
Biharmonic equations
Singular nonlinearity

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10.1090/S0002-9939-2014-11895-8

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title = "Revisiting the Biharmonic equation modelling electrostatic actuation in lower dimensions",

abstract = "Let B ⊂ ℝN be the unit ball. We study the structure of solutions to the semilinear biharmonic problem [formula presented] where p, λ > 0, which arises in the study of the deflection of charged plates in electrostatic actuators. We study in particular the structure of solutions for N = 2 or 3 and show the existence of mountain-pass solutions under suitable conditions on p. Our results contribute to completing the picture of solutions in previous works. Moreover, we also analyze the asymptotic behavior of the constructed mountain-pass solutions as λ → 0.",

keywords = "Asymptotic analysis, Biharmonic equations, Singular nonlinearity",

author = "Zongming Guo and Baishun Lai and Dong Ye",

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T1 - Revisiting the Biharmonic equation modelling electrostatic actuation in lower dimensions

AU - Guo, Zongming

AU - Lai, Baishun

AU - Ye, Dong

PY - 2014/6/1

Y1 - 2014/6/1

N2 - Let B ⊂ ℝN be the unit ball. We study the structure of solutions to the semilinear biharmonic problem [formula presented] where p, λ > 0, which arises in the study of the deflection of charged plates in electrostatic actuators. We study in particular the structure of solutions for N = 2 or 3 and show the existence of mountain-pass solutions under suitable conditions on p. Our results contribute to completing the picture of solutions in previous works. Moreover, we also analyze the asymptotic behavior of the constructed mountain-pass solutions as λ → 0.

AB - Let B ⊂ ℝN be the unit ball. We study the structure of solutions to the semilinear biharmonic problem [formula presented] where p, λ > 0, which arises in the study of the deflection of charged plates in electrostatic actuators. We study in particular the structure of solutions for N = 2 or 3 and show the existence of mountain-pass solutions under suitable conditions on p. Our results contribute to completing the picture of solutions in previous works. Moreover, we also analyze the asymptotic behavior of the constructed mountain-pass solutions as λ → 0.

KW - Asymptotic analysis

KW - Biharmonic equations

KW - Singular nonlinearity

UR - https://www.scopus.com/pages/publications/84901447635

U2 - 10.1090/S0002-9939-2014-11895-8

DO - 10.1090/S0002-9939-2014-11895-8

M3 - 文章

AN - SCOPUS:84901447635

SN - 0002-9939

VL - 142

SP - 2027

EP - 2034

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 6

ER -

Revisiting the Biharmonic equation modelling electrostatic actuation in lower dimensions

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Keywords

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