Electron. J. Diff. Eqns.,
Vol. 2005(2005), No. 146, pp. 114.
Multiplicity and symmetry breaking for positive radial
solutions of semilinear elliptic equations modelling
MEMS on annular domains
Peng Feng, Zhengfang Zhou
Abstract:
The use of electrostatic forces to provide actuation is a method
of central importance in microelectromechanical system (MEMS)
and in nanoelectromechanical systems (NEMS).
Here, we study the electrostatic deflection of an annular
elastic membrane. We investigate the exact number of positive
radial solutions and nonradially symmetric bifurcation for the model
where
.
The exact number of positive radial solutions maybe 0, 1, or 2
depending on
.
It will be shown that the upper branch of radial solutions
has nonradially symmetric bifurcation at infinitely many
. The proof of the multiplicity
result relies on the characterization of the shape of the timemap.
The proof of the bifurcation result relies on a wellknown theorem
due to Kielhofer.
Submitted August 10, 2005. Published December 12, 2005.
Math Subject Classifications: 35J65, 35J60, 35B32.
Key Words: Radial solution; symmetry breaking; multiplicity; MEMS.
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Peng Feng
Department of Mathematics
Michigan State University
East Lansing, MI 48824, USA
email: fengpeng@math.msu.edu 

Zhengfang Zhou
Department of Mathematics
Michigan State University
East Lansing, MI 48824, USA
email: zfzhou@math.msu.edu 
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