Communications in Mathematical Sciences

Volume 15 (2017)

Number 8

Integrability and asymptotic behaviors of positive solutions for some integral equations

Pages: 2099 – 2120

DOI: https://dx.doi.org/10.4310/CMS.2017.v15.n8.a1

Authors

Jiankai Xu (College of Science and Center of Mathematical Modeling and Data Processing in Agriculture, Hunan Agriculture University, Hunan, China)

Huoxiong Wu (School of Mathematical Sciences, Xiamen University, Fujian, Xiamen, China)

Zhong Tan (School of Mathematical Sciences, Xiamen University, Fujian, Xiamen, China)

Abstract

In this paper, we investigate the integrability and asymptotic behaviors of positive solutions for a nonlinear integral system in a functional setting. Using the regularity lifting lemma and some delicate analysis techniques, we obtain the optimal integral intervals and the asymptotic estimates for such solutions around the origin and near infinity. Moreover, the index of regular solution is distinct from one of the previous several related systems.

Keywords

integral system, positive solutions, integrability, asymptotic behaviors, regularity lifting lemma

2010 Mathematics Subject Classification

45E10, 45G05, 45G15, 45M99

Full Text (PDF format)

The research was supported by NSFC (Grant Nos. 11126148, 11671086, 11371295 and 11471041), the NSF of Fujian Province of China grant 2015J01025 and the Project Supported by Scientific Research Fund of Hunan Provincial Education Department (No. 16C0763).

Received 14 December 2016

Accepted 6 May 2017

Published 20 December 2017