Feng, PengZhou, Zhengfang2021-07-142021-07-142005-12-12Feng, 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. 1-14.1072-6691https://hdl.handle.net/10877/13871The 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.Text14 pages1 file (.pdf)enAttribution 4.0 InternationalRadial solutionSymmetry breakingMultiplicityMEMSArticle