The applications of Saddle point theorem to Dirichlet boundary value problem of differential system

We study in this paper the Dirichlet boundary value problem of second-order differential system in the form where u ∈ Rn,A,B ∈ Rn,M ∈ Rn × n is a symmetric matrix, F : [0,1] × Rn Rn such a system comes from a model describing the vibration of a multi-storey building. By using the saddle point theorem, we prove an existence theorem for the solutions to the given system. Copyright © 2014 John Wiley & Sons, Ltd.