Multiplicity and symmetry breaking for positive radial solutions of semilinear elliptic equations modelling MEMS on annular domains
| dc.contributor.author | Feng, Peng | |
| dc.contributor.author | Zhou, Zhengfang | |
| dc.date.accessioned | 2021-07-14T13:07:26Z | |
| dc.date.available | 2021-07-14T13:07:26Z | |
| dc.date.issued | 2005-12-12 | |
| 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.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 14 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Feng, P., & Zhou, Z. (2005). Multiplicity and symmetry breaking for positive radial solutions of semilinear elliptic equations modelling MEMS on annular domains. <i>Electronic Journal of Differential Equations, 2005</i>(146), pp. 1-14. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/13871 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University-San Marcos, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2005, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. | |
| dc.subject | Radial solution | |
| dc.subject | Symmetry breaking | |
| dc.subject | Multiplicity | |
| dc.subject | MEMS | |
| dc.title | Multiplicity and symmetry breaking for positive radial solutions of semilinear elliptic equations modelling MEMS on annular domains | |
| dc.type | Article |