Shamsudinov F.M. On an overdetermined system of second order diffirential equations with singular point

Shamsudinov Fayzullo Mamadulloеvich
Candidate of Physical and Mathematical Sciences, Associate Professor,
Department of Mathematical Analysis, Qurghonteppa State University
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Ayni St., 67, 735140 Qurghonteppa, Tajikistan
Abstract. In this paper we consider the over determined system of second order differential equations with a singular point. The system of equations (1) consists of a hyperbolic equation and one partial differential equation of second order with a singular point. The first equation of 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 equation, we obtain the compatibility conditions for the coefficients and right-hand sides. On the basis of the conditions of independence from the left side of the variable y, to determine any function φ1(x), we obtain an ordinary differential equation of the first order. Another arbitrary function ψ1(y) is determined from the condition of the independence of the left part at the appropriate, passing to the limit.Thus, the obtained representing the solution manifold system using a single arbitrary function of one independent variable y and one arbitrary constant study of properties of the solutions, as well as consider the problem of А.
Key words: over determined system, singular equation, rectangle, variety of solutions, singular point.

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On an Overdetermined System of Second Order Diffirential 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. №5 (24) 2014 pp. 46-54
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