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The existence of nonregular points in a foreign debt model. (English. Russian original) Zbl 0883.90034

Differ. Equations 32, No. 12, 1695-1696 (1996); translation from Differ. Uravn. 32, No. 12, 1701-1702 (1996).
In the short paper, the author describes the economic dynamics of the normed external debt \(d(t)\) by the equation \(\dot d=\alpha d- e+i_c+i_k\), \(t\in[0, T]\), where \(\alpha\) is a constant, \(i_k\) is the investment in import, \(e\) is the volume of export, and \(i_c\) is the consumption of imported goods. The optimization problem to be solved is to find controls \(e^0(t)\), \(i^0_k(t)\) and \(i^0_c(t)\) under some additional constraints, so that \(d(T)\to\min\). An explicit form of optimal controls is found and their economic interpretation is given. Moreover, the relations determining nonregular points are obtained.

MSC:

91B62 Economic growth models
93C95 Application models in control theory
49J15 Existence theories for optimal control problems involving ordinary differential equations
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