Multiplicity of positive solutions to nonlinear systems of Hammerstein integral equations with weighted functions

Xiyou Cheng; Zhaosheng Feng; Zhitao Zhang

doi:10.3934/cpaa.2020012

Article Contents

2020, Volume 19, Issue 1: 221-240. Doi: 10.3934/cpaa.2020012

This issue Previous Article The continuous morbidostat: A chemostat with controlled drug application to select for drug resistance mutants Next Article Positive solutions for the one-dimensional singular superlinear

$ p $

-Laplacian problem

Multiplicity of positive solutions to nonlinear systems of Hammerstein integral equations with weighted functions

1.
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China
2.
Department of Mathematics, University of Texas Rio Grande Valley, Edinburg, TX 78539, USA
3.
Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, China

Received: November 2018

Revised: March 2019

Published: July 2019

This work is supported by NSF of China under 11325107 and 11471148

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Abstract

We are concerned with the existence and multiplicity of component-wise positive solutions for nonlinear system of Hammerstein integral equations with the weighted functions and the associated nonlinear eigenvalue problem. Our discussions are based on the product formula of fixed point index on product cones and the fixed point index theory. Moreover, we establish the existence and multiplicity of component-wise positive solutions for the associated nonlinear systems of second-order ordinary differential equations under the mixed boundary value conditions.

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Mathematics Subject Classification: 45G15, 37C25, 47H30.

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