Nonlinear Spectrum and Fixed Point Index for a Class of Decomposable Operators

Shugui Kang, Yanlei Zhang and Wenying Feng
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Shugui Kang: The Institute of Applied Mathematics, Shanxi Datong University, Datong 037009, China
Yanlei Zhang: Department of Mathematics and Statistics, Queen’s University, Kingston, ON K7L 3N6, Canada
Wenying Feng: Departments of Mathematics and Computer Science, Trent University, Peterborough, ON K9L 0G2, Canada

Mathematics, 2021, vol. 9, issue 3, 1-9

Abstract: We study a class of nonlinear operators that can be written as the composition of a linear operator and a nonlinear map. We obtain results on fixed point index based on parameters that are related to the definitions of nonlinear spectra. As a particular case, existence of positive solutions for a second-order differential equation with separated boundary conditions is proved. The result also provides a spectral interval for the corresponding Hammerstein integral operator.

Keywords: boundary value problem; cone; fixed point index; nonlinear spectrum; stably-solvable map (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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