Positive pseudo almost periodic solutions for some nonlinear infinite delay integral equations

We state sufficient conditions for the existence of positive pseudo almost periodic and asymptotically almost periodic solutions of the following nonlinear infinite delay integral equation: x ( t ) = ∫ − ∞ t a ( t , t − s ) f ( s , x ( s ) ) d s . Then we apply these results to a finite delay integr...

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Veröffentlicht in:	Mathematical and computer modelling 2009-02, Vol.49 (3), p.721-739
Hauptverfasser:	Ait Dads, El Hadi, Cieutat, Philippe, Lhachimi, Lahcen
Format:	Artikel
Sprache:	eng
Schlagworte:	Almost periodic solutions Asymptotically almost periodic solutions Classical Analysis and ODEs Delay differential equation Delay integral equation Exact sciences and technology Integral equations Mathematical analysis Mathematics Methods of scientific computing (including symbolic computation, algebraic computation) Numerical analysis. Scientific computation Ordinary differential equations Pseudo almost periodic solutions Sciences and techniques of general use
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Zusammenfassung:	We state sufficient conditions for the existence of positive pseudo almost periodic and asymptotically almost periodic solutions of the following nonlinear infinite delay integral equation: x ( t ) = ∫ − ∞ t a ( t , t − s ) f ( s , x ( s ) ) d s . Then we apply these results to a finite delay integral equation when the delay is time-dependent and to a delay differential equation.
ISSN:	0895-7177 1872-9479
DOI:	10.1016/j.mcm.2008.07.008