Electron. J. Differential Equations, Vol. 2019 (2019), No. 79, pp. 1-11.

Existence of positive solutions for a nonlinear quadratic integral equation

Chu-Hang Wang, Hui-Sheng Ding, Gaston M. N'Guerekata

Abstract:
In this article, we study the existence of positive solutions for the nonlinear quadratic integral equation
$$ x(t)=g(t,x(t))\int_{-\infty}^{t}a(t,t-s)f(s,x(s))ds,\quad t\in\mathbb{R}. $$
By using fixed point theory on cones, we prove the existence and uniqueness of bounded and continuous solution with positive infimum. An example illustrates the abstract result.

Submitted April 15, 2018. Published June 10, 2019.
Math Subject Classifications: 45G10, 34K37.
Key Words: Quadratic integral equation; positive solution; cone.

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Chu-Hang Wang
College of Mathematics and Information Science
Jiangxi Normal University
Nanchang, Jiangxi 330022, China
email: 2227016700@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'Guerekata
Department of Mathematics
Morgan State University
1700 E. Cold Spring Lane
Baltimore, MD 21251, USA
email: Gaston.N'Guerekata@morgan.edu

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