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Functional Analysis and Its Applications

, Volume 51, Issue 4, pp 306–309 | Cite as

On real solutions of systems of equations

  • V. V. Kozlov
Brief Communications
  • 33 Downloads

Abstract

Systems of equations f 1 = ··· = f n−1 = 0 in ℝ n = {x} having the solution x = 0 are considered under the assumption that the quasi-homogeneous truncations of the smooth functions f 1,..., f n−1 are independent at x ≠ 0. It is shown that, for n ≠ 2 and n ≠ 4, such a system has a smooth solution which passes through x = 0 and has nonzero Maclaurin series.

Key words

quasi-homogeneous truncation asymptotic solution 

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© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia
  2. 2.RUDN UniversityMoscowRussia

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