Open AccessOn conditions of solvability of three-dimensional integralsystem in quadratures
Author(s) -
E. A. Sozontova
Publication year - 2015
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2015-21-10-40-46
Subject(s) - mathematics , space (punctuation) , reduction (mathematics) , order (exchange) , mathematical analysis , pure mathematics , geometry , computer science , finance , economics , operating system
In this paper we consider the system of equations with partial integrals in three-dimensional space. The purpose is to nd sucient conditions of solvability of this system in quadratures. The proposed method is based on the reduction of the original system, rst, to the Goursat problem for a system of dierential equations of the rst order, and after that to the three Goursat problems for dierential equations of the third order. As a result, the sucient conditions of solvability of the considering system in explicit form were obtained. The total number of cases discussing solvability is 16.