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Positive solutions for a system of nonlinear singular Hammerstein integral equations via nonnegative matrices and applications

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Abstract

We are concerned with the existence and multiplicity of positive solutions for the system of nonlinear singular Hammerstein integral equations

$$u_i(t)=\int_a^bk_i(t,s)g_i(s)f_i(s,u_1(s),\ldots,u_n(s)) {\rm d} s,\quad i=1,2,\ldots,n.$$

We use fixed point index theory to establish our main results based on a priori estimates achieved by utilizing nonnegative matrices. As applications, the main results are applied to establish the existence and multiplicity of positive solutions for an elliptic system in an annulus.

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Authors and Affiliations

  1. Department of Mathematics, Qingdao Technological University, Qingdao, Shandong, 266033, People’s Republic of China

    Zhilin Yang

  2. Academy of Mathematics and Systems Science, Institute of Mathematics, Chinese Academy of Sciences, Beijing, 100080, People’s Republic of China

    Zhitao Zhang

Authors
  1. Zhilin Yang
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  2. Zhitao Zhang
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Correspondence to Zhilin Yang.

Additional information

Supported by the NNSF of China (Grants 10871116, 10971179, 10831005 and 10971046).

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Yang, Z., Zhang, Z. Positive solutions for a system of nonlinear singular Hammerstein integral equations via nonnegative matrices and applications. Positivity 16, 783–800 (2012). https://doi.org/10.1007/s11117-011-0146-4

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