Electron. J. Differential Equations, Vol. 2017 (2017), No. 02, pp. 1-10.

Positive almost periodic solutions to integral equations with superlinear perturbations via a new fixed point theorem in cones

Jing-Yun Zhao, Hui-Sheng Ding, Gaston M. N'Guerekata

Abstract:
In this article, we establish a new fixed point theorem for nonlinear operators with superlinear perturbations in partially ordered Banach spaces, Then we use the fixed point theorem to prove the existence of positive almost periodic solutions to some integral equations with superlinear perturbations. Also, a concrete example is given to illustrate our results.

Submitted June 7, 2016. Published January 4, 2017.
Math Subject Classifications: 45G10, 34K14.
Key Words: Almost periodic; delay integral equation; positive solution; superlinear perturbation.

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Jing-Yun Zhao
College of Mathematics and Information Science
Jiangxi Normal University
Nanchang, Jiangxi 330022, china
email: 1475551804@qq.com
Hui-Sheng Ding
College of Mathematics and Information Science
Jiangxi Normal University
Nanchang, Jiangxi 330022, china
email: dinghs@mail.ustc.edu.cn
Gaston M. N'Guérékata
Department of Mathematics
Morgan State University
1700 E. Cold Spring Lane
Baltimore, MD 21251, USA
email: Gaston.N'Guerekata@morgan.edu, nguerekata@aol.com

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