Local existence and regularity of solutions for some partial functional integrodifferential equations with infinite delay in Banach spaces

• Published in: Nonlinear analysis Vol. 70; no. 9; pp. 3378 - 3389
• Main Authors: Ezzinbi, Khalil, Toure, Hamidou, Zabsonre, Issa
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 01.05.2009; Elsevier
• Subjects: Difference and functional equations, recurrence relations; Exact sciences and technology; Finite differences and functional equations; Functional analysis; Infinite delay; Integral equations; Integrodifferential equation; Mathematical analysis; Mathematics; Mild and strict solutions; Numerical analysis; Numerical analysis. Scientific computation; Resolvent operator; Sciences and techniques of general use; Semigroup; 34K30; Semigroup; Resolvent operator; Integrodifferential equation; Infinite delay; Mild and strict solutions; Existence of solution; Nonlinear analysis; Functional equation; Banach space; Delay equation; Local existence; Resolvent; Mathematical model; 34K30 Integrodifferential equation
• ISSN: 0362-546X; 1873-5215
• DOI: 10.1016/j.na.2008.05.006

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.