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Funktsional. Anal. i Prilozhen., 2017, Volume 51, Issue 4, Pages 79–83 (Mi faa3488)  

Brief communications

On real solutions of systems of equations

V. V. Kozlovab

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
b RUDN University, Moscow, Russia

Abstract: Systems of equations $f_1=\cdots=f_{n-1}=0$ в $\mathbb R^n=\{x\}$ in $\mathbb R^n=\{x\}$ having the solution $x=0$ are considered under the assumption that the quasi-homogeneous truncations of the smooth functions $f_1=\cdots=f_{n-1}$ are independent at $x\ne0$. It is shown that, for $n\ne2$ and $n\ne4$, such a system has a smooth solution which passes through $x=0$ and has nonzero Maclaurin series.

Keywords: quasi-homogeneous truncation, asymptotic solution.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 01.A03.21.0008
This work was supported by the Ministry of Education and Science of Russian Federation (contract No. 01.A03.21.0008).


DOI: https://doi.org/10.4213/faa3488

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English version:
Functional Analysis and Its Applications, 2017, 51:4, 306–309

Bibliographic databases:

Document Type: Article
UDC: 517.9
Received: 16.12.2016
Revised: 15.03.2017

Citation: V. V. Kozlov, “On real solutions of systems of equations”, Funktsional. Anal. i Prilozhen., 51:4 (2017), 79–83; Funct. Anal. Appl., 51:4 (2017), 306–309

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