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EPRC is a leading institute in Europe for comparative research on public policy, with a particular focus on regional development policies. Spanning 30 European countries, EPRC research programmes have a strong emphasis on applied research and knowledge exchange, including the provision of policy advice to EU institutions and national and sub-national government authorities throughout Europe.

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Variational principles for eigenvalues of block operator matrices

Langer, H. and Langer, M. and Tretter, Christiane (2002) Variational principles for eigenvalues of block operator matrices. Indiana University Mathematics Journal, 51 (6). pp. 1427-1460. ISSN 0022-2518

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Abstract

In this paper variational principles for block operator matrices are established which are based on functionals associated with the quadratic numerical range. These principles allow to characterize, e.g., eigenvalues in gaps of the essential spectrum and to derive two-sided eigenvalue estimates in terms of the spectral characteristics of the entries of the block operator matrix. The results are applied to a second order partial differential equation depending on the spectral parameter nonlinearly.