Nonlocal Dynamic Problems with Singular Nonlinearities and Applications to MEMS

We establish existence and regularity results for a time dependent fourth order integro-differential equation with a possibly singular nonlinearity which has applications in designing MicroElectroMechanicalSystems. The key ingredient in our approach, besides basic theory of hyperbolic equations in Hilbert spaces, exploit near operator theory introduced by Campanato. \keywords{Singular nonlinear problems \and Nonlocal differential equations \and Higher order hyperbolic PDE \and Regularity results \and Steklov boundary conditions \and Near operators theory\and MEMS.}