Generalized implicit function theorems when the derivative has no bounded inverse

DOI10.1016/0362-546X(82)90023-2zbMath0486.58004OpenAlexW2032348040MaRDI QIDQ3946828

M. Zuhair Nashed, Bruce D.Craven

Publication date: 1982

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(82)90023-2

zbMATH Keywords

bifurcationHammerstein integral equationslocal solvabilityNemytskii operatorimplicit function theorem in Banach spacesapproximate outer inverseapproximate right inversecone inequalityquasi-Newton sequencestrong Frechet differentiabilitystrong Hadamard differential

Mathematics Subject Classification ID

Equations involving nonlinear operators (general) (47J05) Other nonlinear integral equations (45G10) Implicit function theorems, Jacobians, transformations with several variables (26B10) Implicit function theorems; global Newton methods on manifolds (58C15)

Related Items (16)

Differential-Algebraic Equations from a Functional-Analytic Viewpoint: A Survey ⋮ Implicit function theorems, approximate solvability of nonlinear equations, and error estimates ⋮ Operator-theoretic and regularization approaches to ill-posed problems ⋮ Bifurcation from characteristic values of arbitrary multiplicity ⋮ On a general iterative scheme for newton-type methods ⋮ Controllability questions for nonlinear systems in abstract spaces ⋮ Periodic solutions to Maxwell equations in nonlinear media ⋮ Controllability results for the Moore-Gibson-Thompson equation arising in nonlinear acoustics ⋮ Rotating wave solutions to lattice dynamical systems II: persistence results ⋮ An application for an implicit function theorem of Craven and Nashed: continuum limits of lattice differential equations ⋮ Open mappings theorems and linearization stability ⋮ A note on the perturbation of an outer inverse ⋮ Ill-Posed Problems: Operator Methodologies of Resolution and Regularization ⋮ Kink solutions of the classical anisotropic XY chain ⋮ A global implicit function theorem without initial point and its applications to control of non-affine systems of high dimensions ⋮ Some inverse mapping theorems

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