Application of Index Theory in the Study of Special Points of Differential Equations
2021, Articles
2021

Application of Index Theory in the Study of Special Points of Differential Equations

Articles
Објављено 2022-01-06
Khusanov Bazar
Associate Professor of the Higher mathematics department of Samarkand architecture and civil engineering institute, Samarkand, Usbekistan
Fatkhullayev Fakhriddin
Senior teacher of the Higher mathematics department of Samarkand architecture and civil engineering institute, Samarkand, Usbekistan

Сажетак

This article studies the joint existence of singular points of a system of the form where  and and are homogeneous polynomials of degree n with constant coefficients . For this purpose the index theory is applied and the characteristics of a singular point are calculated.

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Референце

Khusanov B., Sharipov S.R., Mamashev S.Kh. On some questions of the trajectory of an n-dimensional generalized homogeneous differential system. -Izv. of the Academy of Sciences of the Kazakh SSR. Series of physical and mathematical sciences, 1981, №3, pp.38-43.

Khusanov B. On the distribution of singular points of one system in n-dimensional space. -Dokl. of the Academy of Sciences of the Uzbek SSR, 1982, No.2, pp.4-6

Nemytsky V.V., Stepanov V.V. Qualitative theory of differential equations. GITTL, M.-L., 1949.