Show simple item record

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.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.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/13871
dc.description.abstract

The 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.formatText
dc.format.extent14 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University-San Marcos, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2005, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectRadial solutionen_US
dc.subjectSymmetry breakingen_US
dc.subjectMultiplicityen_US
dc.subjectMEMSen_US
dc.titleMultiplicity and symmetry breaking for positive radial solutions of semilinear elliptic equations modelling MEMS on annular domainsen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


Download

Thumbnail

This item appears in the following Collection(s)

Show simple item record