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Volume 9
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10.3390/math9030278
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Article

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

by
Shugui Kang
1,
Yanlei Zhang
2 and
Wenying Feng
3,*
1
The Institute of Applied Mathematics, Shanxi Datong University, Datong 037009, China
2
Department of Mathematics and Statistics, Queen’s University, Kingston, ON K7L 3N6, Canada
3
Departments of Mathematics and Computer Science, Trent University, Peterborough, ON K9L 0G2, Canada
*
Author to whom correspondence should be addressed.
Mathematics 2021, 9(3), 278; https://doi.org/10.3390/math9030278
Submission received: 28 December 2020 / Revised: 28 January 2021 / Accepted: 28 January 2021 / Published: 31 January 2021
(This article belongs to the Special Issue Advances in Nonlinear Spectral Theory)
Versions Notes

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 boundary value problem; cone; fixed point index; nonlinear spectrum; stably-solvable map

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MDPI and ACS Style

Kang, S.; Zhang, Y.; Feng, W. Nonlinear Spectrum and Fixed Point Index for a Class of Decomposable Operators. Mathematics 2021, 9, 278. https://doi.org/10.3390/math9030278

AMA Style

Kang S, Zhang Y, Feng W. Nonlinear Spectrum and Fixed Point Index for a Class of Decomposable Operators. Mathematics. 2021; 9(3):278. https://doi.org/10.3390/math9030278

Chicago/Turabian Style

Kang, Shugui, Yanlei Zhang, and Wenying Feng. 2021. "Nonlinear Spectrum and Fixed Point Index for a Class of Decomposable Operators" Mathematics 9, no. 3: 278. https://doi.org/10.3390/math9030278

APA Style

Kang, S., Zhang, Y., & Feng, W. (2021). Nonlinear Spectrum and Fixed Point Index for a Class of Decomposable Operators. Mathematics, 9(3), 278. https://doi.org/10.3390/math9030278

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