Geodesic
Existence and the optimal choice of the values of parameters in inequalities guaranteeing the validity of embedding theorems
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part V, Tome 111 (1981), pp. 63-87 Cet article a éte moissonné depuis la source Math-Net.Ru

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For systems of linear algebraic equations with matrix of coefficientsa $a_{ij}$ ($i,j=1,\dots,n$) 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. 
@article{ZNSL_1981_111_a3,
     author = {V. P. Il'in},
     title = {Existence and the optimal choice of the values of parameters in inequalities guaranteeing the validity of embedding theorems},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {63--87},
     year = {1981},
     volume = {111},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1981_111_a3/}
}
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V. P. Il'in. Existence and the optimal choice of the values of parameters in inequalities guaranteeing the validity of embedding theorems. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part V, Tome 111 (1981), pp. 63-87. http://geodesic.mathdoc.fr/item/ZNSL_1981_111_a3/