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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2010, Volume 16, Number 2, Pages 226–237
(Mi timm564)
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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
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
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
Linking options:
https://www.mathnet.ru/eng/timm564 https://www.mathnet.ru/eng/timm/v16/i2/p226
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