Geodesic
Surjectivity results for nonlinear mappings without oddness conditions
Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 1, pp. 15-28

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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.
Classification : 34B10, 34B15, 47H12, 47H15, 47J05, 47J10, 47N20
Keywords: $(K, L, a)$ homeomorphism; $a$-homogeneous operator; $a$-stably solvable map 
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     title = {Surjectivity results for nonlinear mappings without oddness conditions},
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     url = {http://geodesic.mathdoc.fr/item/CMUC_1997__38_1_a1/}
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Feng, W.; Webb, J. R. L. Surjectivity results for nonlinear mappings without oddness conditions. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 1, pp. 15-28. http://geodesic.mathdoc.fr/item/CMUC_1997__38_1_a1/