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IMA Journal of Applied Mathematics 1978 21(1):95-115; doi:10.1093/imamat/21.1.95
© 1978 by Institute of Mathematics and its Applications
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Dual Extremum Principles for Non-negative Unsymmetric Operators

I. HERRERA and M. J. SEWELL

National University of Mexico
Department of Mathematics, University of Reading

Dual extremum principles are constructed for non-negative unsymmetric operator equations. The theory is in terms of functional-valued linear operators defined on an infinite-dimensional space which need not even be normed. Saddle operators and saddle functional are constructed as essential ingredients. An extension to affine sub-spaces required for certain partial differential equations is included. New dual extremum principles for versions of the heat equation and the wave equation are stated in illustration.


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