Английский
Тоҷикӣ 
Русский 
2021
REPRESENTATION FORMULA OF THE GENERAL SOLUTION AND BOUNDARY VALUE PROBLEM FOR A SYSTEM OF THE TOO ORDER LINEAR ORDINARY DIFFERENTIAL EQUATIONS WITH INTERNAL SINGULAR POINT
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Olimi Abdumanon Gaforzoda REPRESENTATION FORMULA OF THE GENERAL SOLUTION AND BOUNDARY VALUE PROBLEM FOR A SYSTEM OF THE TOO ORDER LINEAR ORDINARY DIFFERENTIAL EQUATIONS WITH INTERNAL SINGULAR POINT 37
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
A system of linear ordinary differential equations of the second order of general form with an internal singular point is investigated. 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 task of studying this system is to study previously considered similar systems with a boundary singular point. Using the known results, the general solution of the system is written out using the resolvents of the corresponding systems of Volterra integral equations of the second kind with a weak singularity. The obtained representation of the general solution is used to prove its inversion formulas, to study the behavior of solutions in the vicinity of a singular point, to formulate and solve a new type of Cauchy and linear conjugation problems.
KEY WORDS
system of ordinary differential equations,internel singular point, system of Volterra integral equations, general solution, inversion formulas, properties of solutions, Cauchy and linear conjugation types problems.