On nonnegative solutions of systems of linear differential equations with variable coefficients under fuzzy initial data and inhomogeneities

V. L. Khatskevich

Russian Air Force Military Educational and Scientific Center of the "N. E. Zhukovskiy and Yu. A. Gagarin Air Force Academy", Voronezh

Abstract: Systems of linear differential equations with variable coefficients with fuzzy initial data and inhomogeneities are examined. In the case of matrices with nonnegative elements, we prove the existence of strong solutions of homogeneous and inhomogeneous initial problems and periodic solutions. The main attention is paid to the nonnegativity of solutions to the corresponding linear problems. It is established under the additional assumption of nonnegativity of fuzzy initial data and heterogeneities. An application to a dynamic model of input-output balance with fuzzy data is considered.

Keywords: fuzzy linear differential equation, positive solution, fuzzy dynamic model of input-output balance

UDC: 517.926

MSC: 00A71

DOI: 10.36535/2782-4438-2025-243-63-77