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Zbl 0964.45003
Ait Dads, E.; Ezzinbi, K.
Existence of positive pseudo-almost-periodic solution for some nonlinear infinite delay integral equations arising in epidemic problems. (English)
[J] Nonlinear Anal., Theory Methods Appl. 41, No.1-2, A, 1-13 (2000). ISSN 0362-546X

The authors give sufficient conditions for existence and uniqueness of a pseudo-almost-periodic solution of the nonlinear integral equation $$x(t)=\int^t_{-\infty}a(t-s)f\bigl(s,x(s)\bigr)ds.$$ An example is given.
[Zbigniew Binderman (Warszawa)]

MSC 2000:: *45G05 Singular nonlinear integral equations
45M15 Periodic solutions of integral equations
45M20 Positive solutions of integral equations
92D30 Epidemiology

Keywords: infinite delay; epidemic problems; positive solution; existence; uniqueness; pseudo-almost-periodic solution; nonlinear integral equation

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Zentralblatt MATH Berlin [Germany]