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Hindawi Publishing Corporation Advances in Diﬀerence Equations Volume 2010, Article ID 143298, 8 pages doi:10.1155/2010/143298 Research Article On Connection between Second-Order Delay Differential Equations and Integrodifferential Equations with Delay Leonid Berezansky,1 Josef Diblı́k,2, 3 and Zdenĕk Šmarda3 1 Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, 66237, Brno University of Technology, Brno, Czech Republic 3 Department of Mathematics, Faculty of Electrical Engineering and Communication, 61600, Brno University of Technology, Brno, Czech Republic 2 Correspondence should be addressed to Leonid Berezansky, brznsky@cs.bgu.ac.il Received 5 October 2009; Accepted 11 November 2009 Academic Editor: Ağacik Zafer Copyright q 2010 Leonid Berezansky et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The existence and uniqueness of solutions and a representation of solution formulas are studied t for the following initial value problem: ẋt t0 Kt, sxhsds ft, t ≥ t0 , x ∈ Rn , xt ϕt, t < t0 . Such problems are obtained by transforming second-order delay diﬀerential equations ẍt atẋgt btxht 0 to first-order diﬀerential equation ...
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