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Asymptotics of some nonlinear eigenvalue problems modelling a MEMS Capacitor. Part II: multiple solutions and singular asymptotics

2010
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European journal of applied mathematics
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Some nonlinear eigenvalue problems related to the modelling of the steady-state deflection of an elastic membrane associated with a MEMS capacitor under a constant applied voltage are analyzed using formal asymptotic methods. These problems consist of certain singular perturbations of the basic membrane nonlinear eigenvalue problem ∆u = λ/(1 + u) 2 in Ω with u = 0 on ∂Ω, where Ω is the unit ball in R 2 . It is well-known that the radially symmetric solution branch to this basic membrane problem

doi:10.1017/s0956792510000318
fatcat:yhjdtgejhvhc3ky7uirnm672vi