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Orientability of Fredholm families and topological degree for orientable nonlinear Fredholm mappings
Abstract We construct a degree theory for oriented Fredholm mappings of index zero between open subsets of Banach spaces and between Banach manifolds. Our approach is based on the orientation of
Degree theory forC1 Fredholm mappings of index 0
We develop a degree theory forC1 Fredholm mappings of index 0 between Banach spaces and Banach manifolds. As in earlier work devoted to theC2 case, our approach is based upon the concept of parity of
Orientation and the Leray-Schauder Theory for Fully Nonlinear Elliptic Boundary Value Problems
We develop an integer valued degree theory for quasilinear Fredholm maps. This class of maps is large enough so we can place in this framework all fully nonlinear elliptic boundary value problems
Parity and generalized multiplicity
Assuming that X and Y are Banach spaces and a:(a, b) —» ?2?(X, Y) is a path of linear Fredholm operators with invertible endpoints, in (F-Pl) we defined a homotopy invariant of a, a(a, I) G Z2 , the
Spectral Flow and Bifurcation of Critical Points of Strongly Indefinite Functionals
Abstract Our main results here are as follows: Let X λ be a family of 2 π -periodic Hamiltonian vectorfields that depend smoothly on a real parameter λ in [ a ,  b ] and has a known, trivial, branch
ON THE COVERING DIMENSION OF THE SET OF SOLUTIONS OF SOME NONLINEAR EQUATIONS
We prove an abstract theorem whose sole hypothesis is that the degree of a certain map is nonzero and whose conclusions imply sharp, multidimensional continuation results. Applications are given to
A local bifurcation theorem for C1-Fredholm maps
The Krasnosel'skii Bifurcation Theorem is generalized to C - Fredholm maps. Let X and Y be Banach spaces, F: R x X —> Y be C - Fredholm of index 1 and F(X, 0) = 0 . If / C R is a closed, bounded
The fundamental group of the space of linear Fredholm operators and the globalanalysis of semilinear equations
We compute the parity of a path of Fredholm operators in terms of its index bundle. The result is applied to the study of bifurcation of semilinear
Bifurcation of Homoclinics of Hamiltonian Systems
We obtain sufficient conditions for bifurcation of homoclinic trajectories of nonautonomous Hamiltonian vector fields parametrized by a circle, together with estimates for the number of bifurcation
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