This article is cited in 14 papers

On multiperiodic integrals of a linear system with the differentiation operator in the direction of the main diagonal in the space of independent variables

A. A. Kulzhumiyeva^a, Zh. A. Sartabanov<sup>b

a</sup> Department of Physics and Mathematics, M. Utemisov West-Kazakhstan State University, 162 Dostyk St, 090000 Uralsk, Republic of Kazakhstan
^b Department of Fundamental and Applied Mathematics, K. Zhubanov Aktobe Regional State University, 34 A. Moldagulova St, 030000 Aktobe, Republic of Kazakhstan

Abstract: In the general theory of first order partial differential equations one of the effective ways of integration is a common method of finding solutions by the complete integral [4–5]. In this note we propose a method of research of problems of multiperiodic solutions of linear systems of equations with the same differentiation operator in the direction of a vector field, which is based on the results of the study multiperiodicity of their complete integral. Such an approach is not found in earlier studies based on the methods of fundamental works [8–9] on multiperiodic solutions of such systems. The elements of the proposed method are used in [1–3, 6–7]. In this note in order to establish the multiperiodicity of a complete integral Green's function is introduced in the absence of non-trivial integral multiperiodic solutions of homogeneous system.

Keywords and phrases: multiperiodic solution, linear system, differentiation operator.

MSC: 35B10

Received: 03.11.2016

Language: English

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