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Positivity

, Volume 16, Issue 4, pp 783–800 | Cite as

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

  • Zhilin Yang
  • Zhitao Zhang
Article

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.

Keywords

System of nonlinear Hammerstein integral equations Positive solution \({\mathbb{R}^n_+}\) -monotone matrix Elliptic system Positive radial solution 

Mathematics Subject Classification (2010)

45G15 45G05 45M20 47H07 47H11 35J57 15A45 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Department of MathematicsQingdao Technological UniversityQingdaoPeople’s Republic of China
  2. 2.Academy of Mathematics and Systems Science, Institute of MathematicsChinese Academy of SciencesBeijingPeople’s Republic of China

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