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Existence and the optimal choice of the values of parameters in inequalities guaranteeing the validity of embedding theorems

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Abstract

For systems of linear algebraic equations with matrix of coefficientsa ij (i,j=1...,n where

under certain assumptions regarding the form of the matrix and for nonnegative right-hand sides, one establishes necessary and sufficient conditions for the existence of strictly positive solutions. One considers applications in the imbedding theory of functional spaces.

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Authors
  1. V. P. Il'in
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 111, pp. 63–87, 1981.

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Il'in, V.P. Existence and the optimal choice of the values of parameters in inequalities guaranteeing the validity of embedding theorems. J Math Sci 24, 37–55 (1984). https://doi.org/10.1007/BF01230263

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