Some Results Of Nonlocal Stationary MEMS Equation

In this paper,I study a nonlocal electrostatic actuated MEMS equation.In the first part,I introduce the background and derivation of the equation and some research works about this problem;In the second part,I give some known inclusions of the local problem to build the foundation for the nonlocal problem;The third part is the main part of my paper.First,I build a connection between the minimal solution of the local and nonlocal problem.Then I use implicit function theorem to prove an existence theorem about the nonlocal problem,giving a relatively precise description of the bifurcation diagram for the nonlocal problem.In the fourth part,I list some remaining problems and share some ideas about the further research of the nonlocal problem.