Английский
Тоҷикӣ 
Русский 
2022
REPRESENTATION FORMULA OF THE GENERAL SOLUTION AND THE CAUCHY TYPE PROBLEM FOR A SYSTEM OF THE SEKOND ORDER LINEAR ORDINARY DIFFERENTIAL EQUATIONS WITH LEFT OR RIGHT BOUNDARY WEAKLY SINGULAR POINT
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Olimi Abdumanon GaforzodaREPRESENTATION FORMULA OF THE GENERAL SOLUTION AND THE CAUCHY TYPE PROBLEM FOR A SYSTEM OF THE SEKOND ORDER LINEAR ORDINARY DIFFERENTIAL EQUATIONS WITH LEFT OR RIGHT BOUNDARY WEAKLY SINGULAR POINT 44
Authors: Olimi Abdumanon Gaforzoda – 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)
JOURNAL NUMBER: 3(62). YEAR OF ISSUE: 2022. LANGUAGE OF THE ARTICLE: Russian
ANNOTATION
In the article, a system of linear ordinary differential equations of the second order of general form with a boundary weakly singular point is investigated by reducing it to a system of Volterra integral equations of the second kind with a weak singularity. The general solution of the system is written out using the resolvent system of integral equations, which is used to establish inversion formulas of the representation, study the behavior of solutions in the neighborhood of a singular point, find out the correct formulation and a solution to a Cauchy-type problem.
KEY WORDS
system of ordinary differential equations, weakly singular point, system of Volterra integral equations, general solution, inversion formulas, properties of solutions, Cauchy type problem.