J. Nonl. Evol. Equ. Appl. 2019 (1), pp. 1-14, published on September 19, 2019:

Existence of positive bounded solutions to a class of neutral integral equations with product perturbations

C-H. Wang, H-S. Ding

College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi 330022, People’s Republic of China

Received on February 22, 2018
Accepted on April 9, 2018

Communicated by Gaston M. N'Guérékata

Abstract.  In this paper, we study the existence of positive bounded solutions for the following nonlinear integral equation with product perturbation:
x(t) = g(t, x(t)) [α(t) x(t − β) + ∫−∞ta(t, t − s) f(s, x(s)) ds + h(t, x(t))] ,   t ∈ R.
In addition, a concrete example is given to illustrate our existence theorem.
Keywords:nonlinear integral equation, positive solution, product perturbation.
2010 Mathematics Subject Classification:   45G10, 34K37.

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