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Nonregular points in a two-sector economic model of foreign debt. (English. Russian original) Zbl 0944.91040

Differ. Equations 33, No. 12, 1591-1595 (1997); translation from Differ. Uravn. 33, No. 12, 1587-1591 (1997).
The paper is devoted to studying the dynamical model of a two-sector open economic system on the time interval \([0,T]\). The first sector extracts raw materials and primary products, and the second one produces consumer goods and asset-forming products. The export volume is assumed to be provided solely by the first sector. The dynamics of both sectors is defined by their production functions, whereas dynamics of foreign debt depends on such control parameters as the flows of foreign investment and of export and import products. In the considered model the piecewise continuous controls are chosen by minimization of the foreign debt at the final instant \(T\). For a certain case of this optimal control problem the author proves the existence of nonregular points on the optimal trajectory in a finite number. As an example such an optimization problem is reduced to a multipoint boundary value problem for ODEs.

MSC:

91B62 Economic growth models
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
49K15 Optimality conditions for problems involving ordinary differential equations
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