Geodesic
On multiperiodic solutions of perturbed nonlinear autonomous systems with the differentiation operator on a vector field
Eurasian mathematical journal, Tome 12 (2021) no. 1, pp. 68-81

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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. 
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     author = {B. Zh. Omarova and Zh. A. Sartabanov},
     title = {On multiperiodic solutions of perturbed nonlinear autonomous systems with the differentiation operator on a vector field},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2021_12_1_a6/}
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B. Zh. Omarova; Zh. A. Sartabanov. On multiperiodic solutions of perturbed nonlinear autonomous systems with the differentiation operator on a vector field. Eurasian mathematical journal, Tome 12 (2021) no. 1, pp. 68-81. http://geodesic.mathdoc.fr/item/EMJ_2021_12_1_a6/