Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 113, pp. 1-26.

Title: Homeomorphisms and Fredholm theory for perturbations of 
       nonlinear Fredholm maps of index zero with applications

Author: Petronije S. Milojevic (New Jersey Inst. of Tech., Newark, NJ, USA)

Abstract:
 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.

Submitted March 6, 2009. Published September 12, 2009.
Math Subject Classifications: 47H15, 35L70, 35L75, 35J40
Key Words: Nonlinear Fredholm mappings; index zero; homeomorphism;
           Fredholm alternative; potential problems; 
	   nonlinear boundary conditions; quasilinear elliptic equations.