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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2010, Volume 16, Number 2, Pages 226–237 (Mi timm564)  

This article is cited in 6 scientific papers (total in 6 papers)

On solutions with the maximal order of vanishing of nonlinear equations with a vector parameter in sectorial neighborhoods

N. A. Sidorovab, R. Yu. Leont'evb

a Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences
b Institute of Mathematics, Economics and Informatics of Irkutsk State University
Full-text PDF (195 kB) Citations (6)
References:
Abstract: The nonlinear operator equation $B(\lambda)x+R(x,\lambda)=0$ is considered. The linear operator $B(\lambda)$ has no bounded inverse operator for $\lambda=0$. The nonlinear operator $R(x,\lambda)$ is continuous in a neighborhood of zero and $R(0,0)=0$. Sufficient conditions for the existence of a continuous solution $x(\lambda)\to0$ as $\lambda\to0$ in some open set $S$ of a linear normed space $\Lambda$ are obtained. The zero of the space $\Lambda$ belongs to the boundary of the set $S$. A method of constructing a solution with the maximal order of vanishing in a neighborhood of the point $\lambda=0$ is suggested. The zero element is taken as the initial approximation.
Keywords: nonlinear operator equation, branching solutions, minimal branch, regularizers, vector parameter.
Received: 13.11.2009
Bibliographic databases:
Document Type: Article
UDC: 517.988.67
Language: Russian
Citation: N. A. Sidorov, R. Yu. Leont'ev, “On solutions with the maximal order of vanishing of nonlinear equations with a vector parameter in sectorial neighborhoods”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 2, 2010, 226–237
Citation in format AMSBIB
\Bibitem{SidLeo10}
\by N.~A.~Sidorov, R.~Yu.~Leont'ev
\paper On solutions with the maximal order of vanishing of nonlinear equations with a~vector parameter in sectorial neighborhoods
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2010
\vol 16
\issue 2
\pages 226--237
\mathnet{http://mi.mathnet.ru/timm564}
\elib{https://elibrary.ru/item.asp?id=14809459}
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  • https://www.mathnet.ru/eng/timm/v16/i2/p226
  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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