Geodesic
Homeomorphisms and Fredholm theory for perturbations of nonlinear Fredholm maps of index zero with applications
Electronic Journal of Differential Equations, Tome 2009 (2009).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We develop a nonlinear Fredholm alternative theory involving k-ball and k-set perturbations of general homeomorphisms and of homeomorphisms that are nonlinear Fredholm maps of index zero. Various generalized first Fredholm theorems and finite solvability of general (odd) Fredholm maps of index zero are also studied. We apply these results to the unique and finite solvability of potential and semilinear problems with strongly nonlinear boundary conditions and to quasilinear elliptic equations. The basic tools used are the Nussbaum degree and the degree theories for nonlinear $C^1$-Fredholm maps of index zero and their perturbations.
Classification : 47H15, 35L70, 35L75, 35J40
Keywords: nonlinear Fredholm mappings, index zero, homeomorphism, Fredholm alternative, potential problems, nonlinear boundary conditions, quasilinear elliptic equations 
@article{EJDE_2009__2009__a17,
     author = {Milojevi\'c, Petronije S.},
     title = {Homeomorphisms and {Fredholm} theory for perturbations of nonlinear {Fredholm} maps of index zero with applications},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2009},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a17/}
}
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Milojević, Petronije S. Homeomorphisms and Fredholm theory for perturbations of nonlinear Fredholm maps of index zero with applications. Electronic Journal of Differential Equations, Tome 2009 (2009). http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a17/