Existence criteria in some extremum problems involving eigenvalues of elliptic operators

Some existence criteria for a certrain class of extremum problems involving eigenvalues of linear elliptic boundary-value problems (including ones in the form of variational inequalities) are proved. The approach applied admits an extension to the case of extremum problems associated with eigenvalues of nonlinear boundary-value problems. Some applications to optimal structural design and comparisons with results in the literature are given.