Файл	Ном	Сабт карда шуд
Okhunov Nozimjon Kobilovich	INTEGRAL REPRESENTATION OF THE GENERAL SOLUTION AND THE CAUCHY - RIQUIER PROBLEM FOR AN ORDINARY OPERATOR - DIFFERENTIAL EQUATION WITH THREE INTERNAL SUPERSINGULAR POINTS	35

Authors: Okhunov Nozimjon Kobilovich - Senior lecturer mathematical analysis Department named after Professor A. Muksinov under Khujand State University named after academician B.G.Gafurov (Tajikistan Republic, Khujand)

JOURNAL NUMBER: 2(65). YEAR OF ISSUE: 2023. LANGUAGE OF THE ARTICLE: Russian

ANNOTATION

The paper studies an operator - differential equation obtained by  - iteration of a linear ordinary differential operator of the first order with three internal super singular points. An integral representation of the general solution of the equation depending on  - arbitrary constants is obtained. The characteristic equalities for the representation, which are the conversion formulas for it, are established. With the help of the obtained representation, the behavior of solutions of the equation in the vicinity of singular points is studied. It is shown that all solutions of the equation in the vicinity of a singular point, depending on the sign of the limit value of a certain coefficient of the operator, tend to infinity or zero like an exponential function. The obtained representation is used to clarify the correct formulation of Cauchy - Riquier problems with conditions on super singular points and to find their solutions explicitly.

KEY WORDS

ordinary operator - differential equation, internal supersingular points, integral representation of the general solution, inversion formulas of the representation, behavior of solutions, Cauchy - Riquier problems.

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