Glasnik Matematicki, Vol. 49, No. 2 (2014), 395-406.

INTEGRABLE SOLUTIONS OF A NONLINEAR INTEGRAL EQUATION RELATED TO SOME EPIDEMIC MODELS

Azzeddine Bellour, Mahmoud Bousselsal and Mohamed-Aziz Taoudi

Department of Mathematics, Ecole Normale Superieure de Constantine, Constantine, Algeria , 25000, Constantine-Algeria
e-mail: bellourazze123@yahoo.com

Department of Mathematics, Laboratoire d'EDP non linéaires, Ecole Normale Superieure, Vieux Kouba, 16050, Algiers-Algeria
e-mail: Bousselsal55@gmail.com

Université Cadi Ayyad, Centre Universitaire Kalaa des Sraghnas, Kalaa des Sraghnas, Morocco
e-mail: mataoudi@gmail.com


Abstract.   In this paper, we discuss the existence of integrable solutions for a nonlinear integral equation related to some epidemic models. The analysis uses the techniques of measures of noncompactness and relies on an improved version of the Krasnosel'skii fixed point theorem.

2010 Mathematics Subject Classification.   45D05, 45G10, 47H30.

Key words and phrases.   Integral equations, measure of weak noncompactness, fixed point theorem, integrable solutions.


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DOI: 10.3336/gm.49.2.12


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