Analysis Of Non-local Problems From Electrostatic Actuation Of MEMS

In the design of Micro-Electromechanical Systems CMEMS) devices, an important method is called the electrostatic actuation, which is based on an electrostatic-controlled tunablecapacitor. Its basic physical principle has two components: the electrostatic Coulomb law and the elastic deformation relation.In this paper, we introduce the mass-spring model of electrostatic actuation, and also a general electrostatically structure(electrostatic-elastic systems).In this paper, we analyze the semi-linear nonlocal elliptic equationon a bounded domainΩof R~N with Navier boundary conditions. This equation models a simple electrostatic MEMS device and governs the deflection of charged plates in the electrostaticactuators under the pinned boundary conditions.The aim of the work is to discuss the equation under four situations:D = 0 ,χ= 0; D = 0 ,χ≠0; D≠0 ,χ= 0; D≠0 ,χ≠0. We bring four situations into comparison and consider the relationship betweenλand the solutions of the equation. At last, we give an estimate ofλ_χ~* .