MULTIPERIODIC SOLUTIONS OF QUASILINEAR SYSTEMS OF INTEGRO-DIFFERENTIAL EQUATIONS WITH Dc-OPERATOR AND ϵ-PERIOD OF HEREDITARITY
Sartabanov Z.A. Aitenova G.M. Abdikalikova G.A.
2022L.N. Gumilyov Eurasian National University
Eurasian Mathematical Journal
2022#13Issue 186 - 100 pp.
We investigate a quasilinear system of partial integro-di erential equations with the operator of di erentiation in the direction of a vector eld, which describes the process of hereditary propagation with an ϵ-period of heredity. Under some conditions on the input data, conditions for the solvability of the initial problem for a quasilinear system of integro-di erential equations are obtained. On this basis, su cient conditions for the existence of multiperiodic solutions of integro-di erential systems are found under the exponential dichotomy additional assumption on the corresponding homogeneous integro-di erential system. The unique solvability of an operator equation in the space of smooth multiperiodic functions is proved, to which the main question under consideration reduces. Thus, su cient conditions are established for the existence of a unique multiperiodical in all time variables solution of a quasilinear system of integro-di erential equations with the di erentiation operator in the directions of a vector eld and a nite period of hereditarity.
di erentiation operator , hereditarity period , Integro-di erential equation , multiperiodic solution , quasilinear system , vector eld
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Department of Mathematics K. Zhubanov Aktobe Regional State University, 34 A. Moldagulova St, Aktobe, 030000, Kazakhstan
Department of Mathematics K. Zhubanov Aktobe Regional State University
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