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On well-posedness of an initial value problem for nonlinear second-order impulsive integro-differential equations of Volterra type in Banach spaces
Authors:Lishan Liu  Yonghong Wu
Affiliation:a Department of Mathematics, Qufu Normal University, Qufu, Shandong 273165, People's Republic of China
b Department of Mathematics and Statistics, Curtin University of Technology, Box 6845, Perth, Australia
Abstract:In this paper, we develop an existence and uniqueness theorem of the solution to an initial value problems for a class of second-order impulsive integro-differential equations of Volterra type in a real Banach space by using the generalized Banach fixed point theorem. An explicit iterative scheme for the solution and an error estimate of the approximation sequence for the initial value problem are also derived. Two examples are presented to demonstrate the application of our results.
Keywords:Unique solution   Second-order impulsive integro-differential equation   Initial value problem   Generalized Banach fixed point theorem
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