## Differential and Integral Equations

### Existence of positive almost periodic or ergodic solutions for some neutral nonlinear integral equations

#### Abstract

We state sufficient conditions for the existence of the positive, almost periodic or ergodic solutions of the following neutral integral equation: \begin{equation*} x(t)=\gamma x(t-\sigma )+(1-\gamma )\displaystyle\int_{t-\sigma }^{t}f(s,x(s))ds, \end{equation*} where $0\leq \gamma < 1$ and $f:\mathbb R\times \mathbb R^{+}\rightarrow \mathbb{R} ^{+}$ is a continuous map. We also treat the asymptotically, weakly and pseudo almost periodic solutions. Our results do not need the monotonicity of $f(t,.)$.

#### Article information

Source
Differential Integral Equations, Volume 22, Number 11/12 (2009), 1075-1096.

Dates
First available in Project Euclid: 20 December 2012

https://projecteuclid.org/euclid.die/1356019405

Mathematical Reviews number (MathSciNet)
MR2555637

Zentralblatt MATH identifier
1240.42021

Subjects
Primary: 45G10: Other nonlinear integral equations

#### Citation

Ait Dads, E.; Cieutat, P.; Lhachimi, L. Existence of positive almost periodic or ergodic solutions for some neutral nonlinear integral equations. Differential Integral Equations 22 (2009), no. 11/12, 1075--1096. https://projecteuclid.org/euclid.die/1356019405