Abramov, A. P. 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. Reviewer: V.Chernyatin (Szczecin) MSC: 91B62 Economic growth models 93C95 Application models in control theory 49J15 Existence theories for optimal control problems involving ordinary differential equations Keywords:economic dynamics; normed external debt; optimization problem; optimal control PDFBibTeX XMLCite \textit{A. P. Abramov}, Differ. Equations 32, No. 12, 1695--1696 (1996; Zbl 0883.90034); translation from Differ. Uravn. 32, No. 12, 1701--1702 (1996)