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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.

Existence Criteria in Some Extremum Problems Involving Eigenvalues of Elliptic Operators