The DSM (dynamical systems method) is justified for nonlinear operator equations in a Banach space. The main assumption is on the spectral properties of the Fre `chet derivative of the operator at a suitable point. A singular perturbation problem related to the original equation is studied.
โฆ LIBER โฆ
Dynamical Systems Method (DSM) for general nonlinear equations
โ Scribed by A.G. Ramm
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 213 KB
- Volume
- 69
- Category
- Article
- ISSN
- 0362-546X
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Consider an operator equation B(u) ร f = 0 in a real Hilbert space. Let us call this equation ill-posed if the operator B 0 (u) is not boundedly invertible, and well-posed otherwise. The dynamical systems method (DSM) for solving this equation consists of a construction of a Cauchy problem, which ha