Multiplicity and symmetry breaking for positive radial solutions of semilinear elliptic equations modelling MEMS on annular domains

dc.contributor.authorFeng, Peng
dc.contributor.authorZhou, Zhengfang
dc.date.accessioned2021-07-14T13:07:26Z
dc.date.available2021-07-14T13:07:26Z
dc.date.issued2005-12-12
dc.description.abstractThe use of electrostatic forces to provide actuation is a method of central importance in microelectromechanical system (MEMS) and in nano-electromechanical systems (NEMS). Here, we study the electrostatic deflection of an annular elastic membrane. We investigate the exact number of positive radial solutions and non-radially symmetric bifurcation for the model -Δu = λ/(1-u)2 in Ω, u = 0 on ∂Ω, where Ω = {x ∈ ℝ2 : ∊ < |x| < 1}. The exact number of positive radial solutions maybe 0, 1, or 2 depending on λ. It will be shown that the upper branch of radial solutions has non-radially symmetric bifurcation at infinitely many λN ∈ (0, λ*). The proof of the multiplicity result relies on the characterization of the shape of the time-map. The proof of the bifurcation result relies on a well-known theorem due to Kielhöfer.
dc.description.departmentMathematics
dc.formatText
dc.format.extent14 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationFeng, P., & Zhou, Z. (2005). Multiplicity and symmetry breaking for positive radial solutions of semilinear elliptic equations modelling MEMS on annular domains. Electronic Journal of Differential Equations, 2005(146), pp. 1-14.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/13871
dc.language.isoen
dc.publisherTexas State University-San Marcos, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2005, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectRadial solution
dc.subjectSymmetry breaking
dc.subjectMultiplicity
dc.subjectMEMS
dc.titleMultiplicity and symmetry breaking for positive radial solutions of semilinear elliptic equations modelling MEMS on annular domains
dc.typeArticle

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