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Parametric stability of the solutions of the impulsive differential Solow equation with delay and dynamic threshold effects. (English) Zbl 1180.91236

Summary: The framework of the more than 50-years old R. M. Solow growth theory [“A contribution to the theory of economic growth”, Q. J. Econ. 70, no. 1, 65–94 (1956)] and R. M. Solow’s studies on technical change [“Technical change and the aggregate production function”, Rev. Econ. Stat. 39, 312–320 (1957)] have not lost their attraction and have been extended widely into modern growth theories. In this paper, the existence of jumps and threshold effects in German capital intensity is identified. For this reason an extension of the initial Solow equation towards a general impulsive Solow differential equation with a delay function is proposed. This extension is aimed to be applied in modern growth theories, for instance to model the German capital intensity. Sufficient conditions for the parametric stability of the solutions of such systems are investigated. The main results are obtained by applying the Lyapunov method.

MSC:

91B84 Economic time series analysis
34K45 Functional-differential equations with impulses
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