ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Necessary Conditions and Criteria of the Existence of Linear Integral Invariants for Multidimensional Differential Systems


Andrei Pranevich

PhD in phisics and mathematics
Associate Professor
Department of mathematic and software support for economic systems,
Faculty of Economics and Management,
Yanka Kupala State University of Grodno,
Ozeshko str. 22, Grodno, Republic of Belarus, 230023


We consider a system of total differential equations. The criteria for the existence of absolute and relative linear integral invariants of the first order are obtained, the necessary conditions for the existence of autonomous and cylindrical absolute integral invariants of the first order are proved, the analytical relations between absolute linear integral invariants and first integrals are established. For Hamiltonian systems in total differentials these criteria are concretized, the absence of universal absolute linear integral invariants of the first order is proved, the analytical form of universal relative linear integral invariant of the first order is given.



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