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W. Feng, J.R.L. Webb 5KHA?JELEJO HAIKJI BH EA=H =FFECI MEJDKJ @@AII ?@EJEI

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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 non- linear operator equations of the formλT(x)−S(x) =f, whereT is invertible, and T, S satisfy various types of homogeneity conditions. We are able to answer some questions left open by Fuˇc´ık, Neˇcas, Souˇcek, and Souˇcek. We employ the concept of ana-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

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