Existence of nonnegative solutions to Leont\('\)ev's system (Q2713889)
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scientific article; zbMATH DE number 1603153
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Existence of nonnegative solutions to Leont\('\)ev's system |
scientific article; zbMATH DE number 1603153 |
Statements
10 June 2001
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Leont'ev's system
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existence of solutions
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nonnegativity of solutions
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0.8829948
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0.88182545
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0.8812422
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0.8787426
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0.8784052
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Existence of nonnegative solutions to Leont\('\)ev's system (English)
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The authors consider the Leont'ev system modeling the dynamics of a~closed ``input-output'' economy with investments. This system generates the linear equation of Sobolev type NEWLINE\[NEWLINE L\dot x=Mx-y NEWLINE\]NEWLINE with \(L\) and \(M\) the operators generated by some matrices (here \(L\) is degenerate (\(\ker L\neq 0\))).NEWLINENEWLINENEWLINEThe authors study the solvability of the Cauchy problem with condition \(x(0)=x_0\) and deduce conditions for solvability. Furthermore, the authors give conditions for ~\(x\) to be~nonnegative. Note that nonnegativity of solutions is necessary for agreement of this~differential model with some actual economical situation.NEWLINENEWLINEFor the entire collection see [Zbl 0956.00039].
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