Implementation of the Small Parameter Method for Studying Multiperiodic Solutions of Systems with a Diagonal Differentiation Operator
Sartabanov Z. Abdikalikova G.A. Aitenova G.M. Omarova B.Z. Zhumagaziyev A.K.
December 2024Pleiades Publishing
Lobachevskii Journal of Mathematics
2024#45Issue 126594 - 6609 pp.
Abstract: The study is devoted to the application of the small parameter method to the study of the existence of multiperiodic solutions of systems containing small parameter equations with a linear homogeneous partial differential operator with unit coefficients. The operator of the system is called the diagonal differentiation operator of the Euclidean space of independent variables. Such systems, although they have an independent interest in theory in various applications of partial differential equations, they are also a strong tool for studying conditionally periodic solutions of systems of ordinary differential equations. This aspect of the system under consideration is of particular interest to us. Therefore, these systems, both in our considered and in the theory of multi-frequency oscillations, are important as a method for studying conditionally periodic systems of ordinary differential equations. Therefore, such an approach can be called a method for studying conditionally periodic systems of ordinary differential equations with a transition to the study of multiperiodic systems of partial differential equations.
differentiation operator , implicit function , multiperiodicity , periodic characteristic , smal parameter method , vector field
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Zhubanov Aktobe Regional University, Aktobe, 030000, Kazakhstan
Utemisov West Kazakhstan University, Uralsk, 090000, Kazakhstan
Zhubanov Aktobe Regional University
Utemisov West Kazakhstan University
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