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November/December 2009 Existence of positive almost periodic or ergodic solutions for some neutral nonlinear integral equations
E. Ait Dads, P. Cieutat, L. Lhachimi
Differential Integral Equations 22(11/12): 1075-1096 (November/December 2009).

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 $f(t,.)$.

Citation

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E. Ait Dads. P. Cieutat. L. Lhachimi. "Existence of positive almost periodic or ergodic solutions for some neutral nonlinear integral equations." Differential Integral Equations 22 (11/12) 1075 - 1096, November/December 2009.

Information

Published: November/December 2009
First available in Project Euclid: 20 December 2012

zbMATH: 1240.42021
MathSciNet: MR2555637

Subjects:
Primary: 45G10

Rights: Copyright © 2009 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.22 • No. 11/12 • November/December 2009
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