Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 52, pp. 1-16.

Title: Existence and multiplicity of positive solutions to systems of nonlinear
       Hammerstein integral equations

Authors: Xiyou Cheng  (Lanzhou Univ., Lanzhou, Gansu, China)
         Zhaosheng Feng (Univ. of Texas Rio Grande Valley, Edinburg, TX, USA)

Abstract:
 This article studies the existence and multiplicity of  component-wise
 positive solutions for systems of nonlinear Hammerstein  integral equations.
 In this system one nonlinear term is uniformly superlinear
 or uniformly sublinear, and the other is locally uniformly superlinear
 or locally uniformly sublinear.
 Discussions are undertaken by means of the fixed point index theory in cones.
 As applications, we show the existence and multiplicity of component-wise
 positive solutions for systems of second-order ordinary differential equations
 with the Dirichlet boundary value conditions and mixed boundary value conditions,
 respectively.


Submitted March 12, 2018. Published April 19, 2019.
Math Subject Classifications: 45G15, 37C25, 45N05.
Key Words: Hammerstein integral equation; positive solution;
           fixed point index; product cone;  Dirichlet boundary condition.