Local existence and regularity of solutions for some partial functional integrodifferential equations with infinite delay in Banach spaces |
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| Authors: | Khalil Ezzinbi Hamidou Toure Issa Zabsonre |
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| Institution: | 1. Université Cadi Ayyad, Faculté des Sciences Semlalia, Département de Mathématiques, B.P. 2390 Marrakech, Morocco;2. Université de Ouagadougou, Département de Mathématiques, Unité de Recherche et de Formation en Sciences Exactes et Appliquées, B.P. 7021 Ouagadougou 03, Burkina Faso |
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| Abstract: | In this work, we study the existence and regularity of solutions for some partial functional integrodifferential equations with infinite delay in Banach spaces. We suppose that the undelayed part admits a resolvent operator in the sense of Grimmer R. Grimmer, Resolvent operators for integral equations in a Banach space, Transactions of the American Mathematical Society 273 (1982) 333–349]. The delayed part is assumed to be locally Lipschitz. Firstly, we show the existence of the mild solutions. Secondly, we give sufficient conditions ensuring the existence of strict solutions. |
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| Keywords: | 34K30 |
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