Geodesic
Oriented degree of Fredholm maps: finite-dimensional reduction method
Contemporary Mathematics. Fundamental Directions, Functional analysis, Tome 44 (2012), pp. 3-171

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The complete oriented degree theory for proper nonlinear Fredholm zero-index maps and their compact perturbations is constructed by means of a finite-dimensional reduction method. Applications to solvability and bifurcations of boundary-value problems for nonlinear elliptic equations are provided. 
@article{CMFD_2012_44_a0,
     author = {V. G. Zvyagin and N. M. Ratiner},
     title = {Oriented degree of {Fredholm} maps: finite-dimensional reduction method},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {3--171},
     publisher = {mathdoc},
     volume = {44},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2012_44_a0/}
}
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V. G. Zvyagin; N. M. Ratiner. Oriented degree of Fredholm maps: finite-dimensional reduction method. Contemporary Mathematics. Fundamental Directions, Functional analysis, Tome 44 (2012), pp. 3-171. http://geodesic.mathdoc.fr/item/CMFD_2012_44_a0/