Oriented degree of Fredholm maps: finite-dimensional reduction method

DOI10.1007/s10958-015-2211-1zbMath1384.47007OpenAlexW2025442720MaRDI QIDQ895064

N. M. Ratiner, Viktor G. Zvyagin

Publication date: 26 November 2015

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-015-2211-1

zbMATH Keywords

nonlinear differential equationslinear differential equationsdegreeorientationFredholm mapFredholm structure on Banach manifoldglobal bifurcation of solutionperturbations of nonlinear Fredholm maps

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Degree theory for nonlinear operators (47H11) Fixed-point theorems on manifolds (58C30) (Semi-) Fredholm operators; index theories (47A53) Index theory and related fixed-point theorems on manifolds (58J20) Fredholm structures on infinite-dimensional manifolds (58B15) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Boundary value problems for linear higher-order PDEs (35G15)

Related Items (4)

Multivalent guiding function in a problem on existence of periodic solutions of some classes of differential inclusions ⋮ The degree of compact multivalued perturbations of Fredholm mappings of positive index and its application to a certain optimal control problem ⋮ Degree of locally condensing perturbations of Fredholm maps with positive index and applications ⋮ Axiomatization of the degree of Fitzpatrick, Pejsachowicz and Rabier

Cites Work

• Degree theory for \(C^1\) Fredholm mappings of index 0
• Leray-Schauder degree: A half century of extensions and applications
• Elliptic partial differential equations of second order
• The homotopy type of the unitary group of Hilbert space
• A degree theory for locally compact perturbations of Fredholm maps in Banach spaces
• A degree theory for compact perturbations of proper \(C^{1}\) Fredholm mappings of index \(0\)
• Zusammenziehbarkeit der allgemeinen linearen Gruppe des Raumes \(c_ 0\) der Nullfolgen
• Open embeddings of certain Banach manifolds
• Some metrics on the subspaces qf a Banach space
• ON THE ORIENTED DEGREE OF A CERTAIN CLASS OF PERTURBATIONS OF FREDHOLM MAPPINGS, AND ON BIFURCATION OF SOLUTIONS OF A NONLINEAR BOUNDARY VALUE PROBLEM WITH NONCOMPACT PERTURBATIONS
• The degree of Fredholm maps equivariant with respect to the actions of the circle and the torus
• Another approach to elliptic boundary problems
• Degree Theory on Oriented Infinite Dimensional Varieties and the Morse Number of Minimal Surfaces Spanning a Curve in R n . Part I: n ≥4
• NON-LINEAR FREDHOLM MAPS AND THE LERAY-SCHAUDER THEORY
• On the number of simply connected minimal surfaces spanning a curve
• Topologie et équations fonctionnelles
• COMPLEMENTED SUBSPACES IN BANACH SPACES
• An Infinite Dimensional Version of Sard's Theorem
• Differentiable norms in Banach spaces
• Differentiable Functions and Rough Norms on Banach Spaces
• The measure of the critical values of differentiable maps
• On the concept of orientability for Fredholm maps between real Banach manifolds
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