O ct 2 00 4 Dynamical systems method ( DSM ) for nonlinear equations in Banach spaces
نویسنده
چکیده
Let F : X → X be a C 2 loc map in a Banach space X, and A be its Frèchet derivative at the element w := w ε , which solves the problem (*) ˙ w = −A −1 ε (F (w) + εw), w(0) = w 0 , where A ε := A + εI. Assume that A −1 ε ≤ cε −k , 0 < k ≤ 1, 0 < ε > ε 0. Then (*) has a unique global solution, w(t), there exists w(∞), and (* *) F (w(∞)) + εw(∞) = 0. Thus the DSM (Dynamical Systems Method) is justified for equation (* *). The limit of w ε as ε → 0 is studied.
منابع مشابه
Dynamical Systems Method (DSM) for solving nonlinear operator equations in Banach spaces
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