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On the number of positive solutions of a nonlinear algebraic system. (English) Zbl 1121.39013

The authors deal with the existence, uniqueness, multiplicity and nonexistence of positive solutions for a nonlinear algebraic system of the form \(X=\lambda AF(x)\), where \(\lambda> 0\) is a parameter, \(x\) and \(F(x)\) are column vectors and \(A= (a_{ij})_{n\times n}\) is an \(n\times n\) square matrix with \(a_{ij}> 0\) \(\forall(ij)\in \{1,2,\dots, n\}\times \{1,2,\dots, n\}\). Examples of such problems from various areas are given, too.

MSC:

39A11 Stability of difference equations (MSC2000)
39A10 Additive difference equations
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