Shamsudinov F.M. On an Overdetermined System of Differential Equations With Singular Point

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https://doi.org/10.15688/jvolsu1.2016.6.9

Fayzullo Mamadulloеvich Shamsudinov
Candidate of Physical and Mathematical Sciences, Associate Professor,
Department of Mathematical Analysis,
Khurghonteppa State University
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Ayni St., 67, 735140 Khurghonteppa, Republic of Tajikistan

Abstract. In this paper we consider the overdetermined system of second order differential equations with a singular point.
The system of equations (1) consists of a hyperbolic equation and two partial differential equations of second order with a singular point. The first equation of the system (1) under certain conditions on the coefficients can be represented as a superposition of two first order differential operators. Solving this equation and substituting its value in the second and third equation to get together conditions on the coefficients and right-hand sides. On the basis of the conditions of independence from the left side of the variable y, to determine the arbitrary function φ₁(x) we obtain the ordinary differential equation of the first order. Other arbitrary function ψ₁(y)  is determined from the condition that the right side of independence in appropriate, limiting transition.
Thus, we obtained representation of the diversity of solutions using two arbitrary constants and studied properties of the resulting decisions.

Key words: singular point, rectangle, variety of solutions, overdetermined system, unknown function.

On an Overdetermined System of Differential Equations With Singular Point by Shamsudinov F.M. is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Science Journal of Volgograd State University. Mathematics. Physics. №6 (37) 2016 pp. 99-107

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