Английский
Тоҷикӣ 
Русский 
2021
REPRESENTATION FORMULA OF A GENERAL SOLUTION AND A CAUCHY - RYKE TYPE PROBLEMS FOR AN ORDINARY DIFFERENTIAL EQUATION OF A SPECIAL TYPE WITH A BOUNDARY AND INTERNAL WEAKLY SINGULAR POINT
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Olimi Abdumanon Gaforzoda REPRESENTATION FORMULA OF A GENERAL SOLUTION AND A CAUCHY - RYKE TYPE PROBLEMS FOR AN ORDINARY DIFFERENTIAL EQUATION OF A SPECIAL TYPE WITH A BOUNDARY AND INTERNAL WEAKLY SINGULAR POINT 31
Authors: Olimi Abdumanon Gaforzoda (Olimov Abdumanon Gaforovich) – Candidate of Physics and Mathematics Sciences, Associate Professor Mathematical Analysis Department named after Professor A. Muksinov under Khujand State University named after academician B.G.Gafurov (Tajikistan Republic, Khujand), Dadojanova Mukaddas Yakubdjanovna - Candidate of Physics and Mathematics Sciences, Associate Professor, Head of Higher and Applied Mathematics Department under Khujand State University named after academician B.G.Gafurov(Tajikistan Republic, Khujand), Okhunov Nozimjon Kobilovich - Senior Lecturer of Mathematical Analysis Department named after Professor A. Muksinov under Khujand State University named after academician B.G.Gafurov (Tajikistan Republic, Khujand), Tolibov Said Ayubdjonovich - Undergraduate Second Year Degree Mathematics of the Khujand State University named after academician B.G.Gafurov (Tajikistan Republic, Khujand)
JOURNAL NUMBER: 1(56). YEAR OF ISSUE: 2021. LANGUAGE OF THE ARTICLE: Tajik
ANNOTATION
The article studies the equation obtained by double iterating an ordinary differential operator of the first order with boundary and internal weakly singular point. Representation formula of the general solution of the equation is found, which is applied to the study of the properties of solutions, their behavior in the neighborhood of a singular point, the formulation and solution of Cauchy - Ryke type problems with conditions at a weakly singular point. It is shown that the solutions of the equation and the value of the corresponding operator from them in the neighborhood of the weakly singular point remain bounded. The presence of a singularity in the equation affects the formulation of boundary value problems and is expressed in the fact that it will be sufficient to set the conditions on a part of the boundary.
KEY WORDS
special type ordinary differential equation, weakly singular point, representation formula of the general solution, behavior of solutions, characteristic equalities, Cauchy - Ryke type problem.