Existence and multiplicity of positive solutions to systems of nonlinear Hammerstein integral equations
Date
2019-04-19
Authors
Cheng, Xiyou
Feng, Zhaosheng
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
Hammerstein integral equation, Positive solution, Fixed point index, Product cone, Dirichlet boundary condition
Citation
Cheng, X., & Feng, Z. (2019). Existence and multiplicity of positive solutions to systems of nonlinear Hammerstein integral equations. <i>Electronic Journal of Differential Equations, 2019</i>(52), pp. 1-16.
Rights
Attribution 4.0 International