Spectral Analysis for a Singular Differential System with Integral Boundary Conditions

Sun, F.; Liu, Lishan; Zhang, Xinguang; Wu, Yong Hong

doi:10.1007/s00009-016-0774-9

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Authors

Sun, F.

Liu, Lishan

Zhang, Xinguang

Wu, Yong Hong

Date

2016

Type

Journal Article

Metadata

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Citation

Sun, F. and Liu, L. and Zhang, X. and Wu, Y.H. 2016. Spectral Analysis for a Singular Differential System with Integral Boundary Conditions. Mediterranean Journal of Mathematics. 13 (6): pp. 4763-4782.

Source Title

Mediterranean Journal of Mathematics

DOI

10.1007/s00009-016-0774-9

ISSN

1660-5446

School

Department of Mathematics and Statistics

URI

http://hdl.handle.net/20.500.11937/52228

Collection

Curtin Research Publications

Abstract

© 2016, Springer International Publishing.In this paper, by constructing a cone K1 × K2 in the Cartesian product space C[0, 1] × C[0, 1], and using spectral analysis of the relevant linear operator for the corresponding differential system, some properties of the first eigenvalue corresponding to the relevant linear operator are obtained, and the fixed-point index of nonlinear operator in the K1 × K2 is calculated explicitly and the existence of at least one positive solution or two positive solutions of the singular differential system with integral boundary conditions is established.