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An optimal lower eigenvalue system. (English) Zbl 1217.49039

Summary: An optimal lower eigenvalue system is studied, and main theorems including a series of necessary and sufficient conditions for the existence and a Lipschitz continuity result concerning stability are obtained. As applications, solvability results to some von-Neumann-type input-output inequalities, growth, and optimal growth factors, as well as Leontief-type balanced and optimal balanced growth paths, are also gotten.

MSC:

49R05 Variational methods for eigenvalues of operators
49K40 Sensitivity, stability, well-posedness
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