Electron. J. Differential Equations, Vol. 2019 (2019), No. 52, pp. 1-16.

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

Xiyou Cheng, Zhaosheng Feng

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.

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Xiyou Cheng
School of Mathematics and Statistics
Lanzhou University
Lanzhou, Gansu 730000, China
email: chengxy@lzu.edu.cn
Zhaosheng Feng
Department of Mathematics
University of Texas Rio Grande Valley
Edinburg, TX 78539, USA
email: zhaosheng.feng@utrgv.edu

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