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Spectral Analysis for a Singular Differential System with Integral Boundary Conditions

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Abstract

In this paper, by constructing a cone K 1 × K 2 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 K 1 × K 2 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.

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Authors and Affiliations

  1. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, Shandong, China

    Fenglong Sun & Lishan Liu

  2. Department of Mathematics and Statistics, Curtin University, Perth, WA, 6845, Australia

    Lishan Liu, Xinguang Zhang & Yonghong Wu

  3. Department of Mathematics and Informational Science, Yantai University, Yantai, 264005, Shandong, China

    Xinguang Zhang

Authors
  1. Fenglong Sun
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  2. Lishan Liu
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  3. Xinguang Zhang
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  4. Yonghong Wu
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Correspondence to Lishan Liu.

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Sun, F., Liu, L., Zhang, X. et al. Spectral Analysis for a Singular Differential System with Integral Boundary Conditions. Mediterr. J. Math. 13, 4763–4782 (2016). https://doi.org/10.1007/s00009-016-0774-9

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  • DOI: https://doi.org/10.1007/s00009-016-0774-9

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