Английский Английский

2022

FORMULA OF THE GENERAL SOLUTION IN INTEGRAL FORM, CAUCHY AND LINEAR CONJUGATION TYPES PROBLEM FOR A SYSTEM OF SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS WITH AN INTERNAL WEAKLY SINGULAR POINT

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Download this file (3-Олими Абдуманон Гафорзода.pdf)Olimi Abdumanon Gaforzoda FORMULA OF THE GENERAL SOLUTION IN INTEGRAL FORM, CAUCHY AND LINEAR CONJUGATION TYPES PROBLEM FOR A SYSTEM OF SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS WITH AN INTERNAL WEAKLY SINGULAR POINT41

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, for a system of linear ordinary differential equations of the second order with an internal weakly singular point, a general solution is found using the resolvents of the corresponding two systems of Volterra integral equations of the second kind with a weak singularity. The resulting formula is used to establish the formulas for inverting the representation, clarifying the formulation and finding solutions of Cauchy and linear conjugation types problem.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          

 

KEY WORDS

system of ordinary differential equations second order,  internal weakly singular point, system of Volterra integral equations, general solution, inversion formulas,Cauchy problem, linear conjugation problem.