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Dynamical Systems Method (DSM) for general nonlinear equations

โœ 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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๐Ÿ“œ SIMILAR VOLUMES


Dynamical systems method (DSM) for nonli
โœ A.G. Ramm ๐Ÿ“‚ Article ๐Ÿ“… 2006 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 116 KB

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.

Dynamical systems method for ill-posed e
โœ A.G. Ramm ๐Ÿ“‚ Article ๐Ÿ“… 2005 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 283 KB

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