## African Diaspora Journal of Mathematics

- Afr. Diaspora J. Math. (N.S.)
- Volume 12, Number 1 (2011), 19-33.

### Positive Pseudo Almost Automorphic Solutions for Some Nonlinear Infinite Delay Integral Equations

P. Cieutat and K. Ezzinbi

#### Abstract

We state sufficient conditions for the existence of positive pseudo almost automorphic solutions of the following nonlinear infinite delay integral equation:

$$ x(t)= \int^t_{-\infty}a(t,t-s)f(s,x(s))\: ds . $$

We deduce some corollaries on a finite delay integral equation and on a delay differential equation.

#### Article information

**Source**

Afr. Diaspora J. Math. (N.S.), Volume 12, Number 1 (2011), 19-33.

**Dates**

First available in Project Euclid: 11 August 2011

**Permanent link to this document**

https://projecteuclid.org/euclid.adjm/1313092839

**Mathematical Reviews number (MathSciNet)**

MR2826839

**Zentralblatt MATH identifier**

1239.45008

**Keywords**

Pseudo almost automorphic solutions delay differential equation delay integral equation Hilbert's projective metric fixed point

#### Citation

Cieutat, P.; Ezzinbi, K. Positive Pseudo Almost Automorphic Solutions for Some Nonlinear Infinite Delay Integral Equations. Afr. Diaspora J. Math. (N.S.) 12 (2011), no. 1, 19--33. https://projecteuclid.org/euclid.adjm/1313092839