Continuity of the eigenvalues for a vibrating beam

In this paper we prove that the eigenvalues of a vibrating beam have a strongly continuous dependence on the elastic destructive force, i.e., the eigenvalues, as nonlinear functionals of the elastic destructive force, are continuous in the elastic destructive force with respect to the weak topologies in the Lebesgue spaces Lp. In virtue of the minimax characterization for eigenvalues, we prove first the continuity of the lowest eigenvalue and then all the eigenvalues by the induction principle.