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The nonlinear non-local elliptic equation governing the deflection of charged plates in electrostatic actuators is studied under the pinned and the clamped boundary conditions. Results concerning the existence, construction and approximation, and behaviour of classical and singular solutions with respect to the variation of physical parameters of the equation in various situations are presented.doi:10.1098/rspa.2007.1816 fatcat:ins6larzjjdcpj4y7jrm6tdo2i