Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 79, pp. 1-11.

Title: Existence of positive solutions for a nonlinear quadratic integral equation

Authors: Chu-Hang Wang  (Jiangxi Normal Univ., Nanchang, Jiangxi, China)
         Hui-Sheng Ding (Jiangxi Normal Univ., Nanchang, Jiangxi, China)
         Gaston M. N'Guerekata (Morgan State Univ., Baltimore, MD, USA)

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.