Formation of a stable price for energy resources by solving a non-linear dynamic problem as an element of socio-economic stability of the economy

Relevance. The authors note that the formation of a stable price for natural resources and the possibility of smoothing the price during fluctuations not only in demand for them, but also changes in the supply schedule for economic and other reasons require the development of an economic model; they are very relevant. The purpose of the study: identifying the possibilities of forecasting energy prices in the event of price fluctuations and the formation of various levels of demand in the market and taking into account market and non-market methods for its regulation. Results of the study. Studying various processes and problems in the field of economics, the authors propose using various types of linear and nonlinear boundary value problems for ordinary differential equations. This paper shows that the theory of boundary value problems for nonlinear differential equations is one of relevant factors in predicting energy prices in the structure of the economic development program. The authors define modeling tasks for the purpose of adjusting energy demand for a long time. This paper notes that the formation of demand for energy resources in addition to the standard time lag, which determines seasonality, also requires adjustment due to the need to formulate the socio-economic task of smoothing demand. Conclusions. The economic and mathematical models presented in the paper are universal and can be used by business entities, state bodies which form the demand and consumption of energy resources in the country. This will contribute to increasing the efficiency of managing the country’s energy complex and ensuring integrated activities focused on making informed and timely decisions in other business facilities.