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Eurasian Mathematical Journal, 2012, том 3, номер 1, страницы 86–96
(Mi emj76)
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Dynamical systems method (DSM) for solving nonlinear operator equations in Banach spaces
A. G. Ramm Kansas State University, Department of Mathematics,
Manhattan, KS 66506-2602, USA
Аннотация:
Let $F(u)=h$ be a solvable operator equation in a Banach space $X$ with a Gateaux differentiable norm. Under minimal smoothness assumptions on $F$, sufficient conditions are given for the validity of the Dynamical Systems Method (DSM) for solving the above operator equation. It is proved that the DSM (Dynamical Systems
Method)
$$
\dot u(t)=-A_{a(t)}^{-1}(u(t))[F(u(t))+a(t)u(t)-f)],\quad u(0)=u_0,
$$
converges to $y$ as $t\to+\infty$, for $a(t)$ properly chosen. Here $F(y)=f$, and $\dot u$ denotes the time derivative.
Ключевые слова и фразы:
nonlinear operator equations, DSM (Dynamical Systems Method), Banach spaces.
Поступила в редакцию: 21.11.2011
Образец цитирования:
A. G. Ramm, “Dynamical systems method (DSM) for solving nonlinear operator equations in Banach spaces”, Eurasian Math. J., 3:1 (2012), 86–96
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/emj76 https://www.mathnet.ru/rus/emj/v3/i1/p86
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Страница аннотации: | 212 | PDF полного текста: | 60 | Список литературы: | 30 |
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