Dynamical systems method (DSM) for selfadjoint operators

DOI10.1016/j.jmaa.2006.06.044zbMath1125.34041OpenAlexW2105247073MaRDI QIDQ864644

Alexander G. Ramm

Publication date: 12 February 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2006.06.044

zbMATH Keywords

selfadjoint operatorill-posed problemsoperator equationsdynamical system method

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Equations and inequalities involving linear operators, with vector unknowns (47A50) Linear differential equations in abstract spaces (34G10) Asymptotic properties of solutions to ordinary differential equations (34D05)

Related Items

THE DYNAMICAL SYSTEMS METHOD FOR SOLVING NONLINEAR EQUATIONS WITH MONOTONE OPERATORS ⋮ Implicit function theorem via the DSM ⋮ How large is the class of operator equations solvable by a DSM Newton-type method? ⋮ A nonlinear inequality and applications ⋮ Dynamical systems method (DSM) for general nonlinear equations ⋮ On unbounded operators and applications ⋮ Dynamical systems method (DSM) for solving equations with monotone operators without smoothness assumptions on \(F{^{\prime}}(u)\) ⋮ An efficient dynamical systems method for solving singularly perturbed integral equations with noise ⋮ Stability of solutions to abstract evolution equations with delay ⋮ DSM for general nonlinear equations ⋮ On a new notion of the solution to an ill-posed problem ⋮ A globally optimal tri-vector method to solve an ill-posed linear system ⋮ A discrepancy principle for equations with monotone continuous operators

Cites Work

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• Theory of linear ill-posed problems and its applications. Transl., updated and revised from the Russian edition 1978
• Dynamical systems method for solving operator equations.
• Regularization of ill-posed problems with unbounded operators
• Dynamical systems method (DSM) for nonlinear equations in Banach spaces