Extremal Eigenvalues of the Sturm-Liouville Problems with Discontinuous Coefficients

In this paper, an extremal eigenvalue problem to the Sturm-Liouville equations withdiscontinuous coefficients and volume constraint is investigated. Liouvilletransformation is applied to change the problem into an equivalent minimizationproblem. Finite element method is proposed and the convergence for the finiteelement solution is established. A monotonic decreasing algorithm is presentedto solve the extremal eigenvalue problem. A global convergence for the algorithmin the continuous case is proved. A few numerical results are given to depict theefficiency of the method.