Английский
Тоҷикӣ 
Русский 
2021
REPRESENTATION OF THE GENERAL SOLUTION IN INTEGRAL FORM AND THE CAUCHY TYPE PROBLEM FOR A SYSTEM OF THE TOO ORDER LINEAR ORDINARY DIFFERENTIAL EQUATIONS WITH BOUNDARY SINGULAR POINT
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Olimi Abdumanon Gaforzoda REPRESENTATION OF THE GENERAL SOLUTION IN INTEGRAL FORM AND THE CAUCHY TYPE PROBLEM FOR A SYSTEM OF THE TOO ORDER LINEAR ORDINARY DIFFERENTIAL EQUATIONS WITH BOUNDARY SINGULAR POINT 16
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)
JOURNAL NUMBER: 4(59). YEAR OF ISSUE: 2021. LANGUAGE OF THE ARTICLE: Russian
ANNOTATION
The article investigates a system of linear ordinary differential equations of the second order of a general form with a boundary singular point. A certain equation of the system is considered the main one and its study is carried out depending on the properties of the coefficient for the corresponding unknown function in this equation. The problem of solving this system is reduced to an equivalent problem of solving a system of Volterra integral equations of the second kind with a weak singularity. The general solution of the system is expressed using the resolvent system of integral equations. The obtained representation is used to establish its inversion formulas, study the behavior of solutions in the neighborhood of a singular point, the correct formulation and solving of the Cauchy problem of a new type.
KEY WORDS
system of ordinary differential equations, singular point, system of Volterra integral equations, general solution, inversion formulas, properties of solutions, Cauchy type problem.