W. Feng, J.R.L. Webb
Surjectivity results for nonlinear mappings without oddness conditions

Comment.Math.Univ.Carolinae 38,1 (1997) 15-28.

Abstract:Surjectivity results of Fredholm alternative type are obtained for nonlinear operator equations of the form ${\lambda } T(x)-S(x)=f$, where $T$ is invertible, and $T,S$ satisfy various types of homogeneity conditions. We are able to answer some questions left open by Fu\v{c}\'{\i }k, Ne\v{c}as, Sou\v{c}ek, and Sou\v{c}ek. We employ the concept of an $a$-{stably-solvable} operator, related to nonlinear spectral theory methodology. Applications are given to a nonlinear Sturm-Liouville problem and a three point boundary value problem recently studied by Gupta, Ntouyas and Tsamatos.

Keywords: $(K,L,a)$ homeomorphism, $a$-homogeneous operator, $a$-stably solvable map
AMS Subject Classification: 47H15, 47H12, 34B10