This article is cited in 3 papers

On multiperiodic solutions of perturbed nonlinear autonomous systems with the differentiation operator on a vector field

B. Zh. Omarova, Zh. A. Sartabanov

Department of Mathematics, K. Zhubanov Aktobe Regional State University, 34 A. Moldagulova St, 030000 Aktobe, Kazakhstan

Abstract: 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.

Keywords and phrases: multiperiodic solutions, autonomous system, differentiation operator, Lyapunov's vector field, perturbation.

MSC: 34C46, 35B10, 35C15, 35F35, 35F50

Received: 14.10.2019

Language: English

DOI: 10.32523/2077-9879-2021-12-1-68-81

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