Non-autonomous nonlinear integro-differential equations with infinite delay

In this paper we consider a non-autonomous abstract nonlinear Volterra integro-differential equation with infinite delay in a Banach space. We establish the existence and uniqueness of a strict solution under a certain local Lipschitz condition on the nonlinear map and an integrability condition on...

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Bibliographic Details
Published in:Nonlinear analysis Vol. 70; no. 7; pp. 2642 - 2653
Main Authors: Bahuguna, D., Pandey, D.N., Ujlayan, A.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Ltd 01.04.2009
Elsevier
Subjects:
Exact sciences and technology
Hyperbolic problem
Infinite delay
Mathematical analysis
Mathematics
Non-autonomous integro-differential equation
Phase space
Sciences and techniques of general use
Non-autonomous integro-differential equation
Infinite delay
Phase space
Hyperbolic problem
Non linear equation
Nonlinear analysis
Hyperbolic equation
Mathematical model
Integrodifferential equation
Partial differential equation
ISSN:0362-546X, 1873-5215
Online Access:Get full text
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Summary:In this paper we consider a non-autonomous abstract nonlinear Volterra integro-differential equation with infinite delay in a Banach space. We establish the existence and uniqueness of a strict solution under a certain local Lipschitz condition on the nonlinear map and an integrability condition on the kernel.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2008.03.051