Glasnik Matematicki, Vol. 51, No. 2 (2016), 413-430.

EXISTENCE RESULTS FOR SOME PARTIAL INTEGRODIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

Khalil Ezzinbi, Saifeddine Ghnimi and Mohamed-Aziz Taoudi

Department of Mathematics, Faculty of Sciences Semlalia, Cadi Ayyad University, BP 2390 Marrakech, Morocco
e-mail: ezzinbi@uca.ma

Department of Mathematics, Faculty of Sciences, University of Gafsa, B.P. 2112 Gafsa, Tunisia
e-mail: ghnimisaifeddine@yahoo.fr

Cadi Ayyad University, National School of Applied Sciences, Marrakech, Morocco
e-mail: a.taoudi@uca.ma


Abstract.   In this work, we study the existence of mild solutions for a class of partial integrodifferential equations with nonlocal conditions. Our analysis uses the resolvent operator theory and relies on a new fixed point theorem of Sadovskii-Krasnosel'skii type. Our results improve and complement several earlier related works. Some examples are provided to illustrate the theoretical results.

2010 Mathematics Subject Classification.   45K05, 47H10, 47D06.

Key words and phrases.   Partial integrodifferential equation, nonlocal conditions, mild solution, fixed point theorem, resolvent operator, semigroup operator.


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DOI: 10.3336/gm.51.2.09


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