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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Shugui Kang & Yanlei Zhang & Wenying Feng, 2021. "Nonlinear Spectrum and Fixed Point Index for a Class of Decomposable Operators," Mathematics, MDPI, vol. 9(3), pages 1-9, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:3:p:278-:d:490351
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