ON MULTIPERIODIC SOLUTIONS OF PERTURBED NONLINEAR AUTONOMOUS SYSTEMS WITH THE DIFFERENTIATION OPERATOR ON A VECTOR FIELD
Omarova B.Z. Sartabanov Z.A.
2021L.N. Gumilyov Eurasian National University
Eurasian Mathematical Journal
2021#12Issue 168 - 81 pp.
A quasilinear system with the differentiation operator with respect to the directions of vector fields specified by Lyapunov’s system with respect to space independent variables and a multiperiodic system with respect to time variables is considered. We study the problem of the existence and uniqueness of a multiperiodic solution of a quasilinear system and we use methods of the theory of multiperiodic solutions of linear systems. The research partially reflects the multiperiodic structure of a solution of the initial problem for quasilinear systems. Conditions for the existence and uniqueness of a multiperiodic solution, an existence theorem of a solution of the initial problem, and the problem of multiperiodic solutions are given. They are proved by the method of contraction mappings defined on spaces of smooth functions.
autonomous system , differentiation operator , Lyapunov’s vector field , multiperiodic solutions , perturbation
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Department of Mathematics, K. Zhubanov Aktobe Regional State University, 34 A. Moldagulova St, Aktobe, 030000, Kazakhstan
Department of Mathematics
10 лет помогаем публиковать статьи Международный издатель
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