A mini max theorem for the quasi-convex functional and the solution of the nonlinear beam equation

In this paper, a definition of a kind of quasi-convex functional was proposed and two properties of the quasi-convex functional were proved. A mini max theorem due to Stepan A. Tersian was generalized by using the properties of the quasi-convex functional. The existence and uniqueness of solution of the boundary value problem for the nonlinear beam equation was probed and an existence and uniqueness theorem was presented.