Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article On Connection between Second-Order Delay Differential Equations and Integrodifferential Equations with Delay | Hindawi Publishing Corporation Advances in Difference Equations Volume 2010 Article ID 143298 8 pages doi 2010 143298 Research Article On Connection between Second-Order Delay Differential Equations and Integrodifferential Equations with Delay Leonid Berezansky 1 Josef Diblik 2 3 and Zdenek Smarda3 1 Department of Mathematics Ben-Gurion University of the Negev Beer-Sheva 84105 Israel 2 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 Correspondence should be addressed to Leonid Berezansky brznsky@ Received 5 October 2009 Accepted 11 November 2009 Academic Editor Agacik Zafer Copyright 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 for the following initial value problem x t f tf K t s x h s ds f t t t0 x e R x t y t t t0. Such problems are obtained by transforming second-order delay differential equations x f a t x g t b t x h t 0 to first-order differential equations. 1. Introduction and Preliminaries The second order delay differential equation x t a t x g t b t x h ty 0 attracts the attention of many mathematicians because of their significance in applications. In particular Minorsky 1 in 1962 considered the problem of stabilizing the rolling of a ship by an activated tanks method in which ballast water is pumped from one position to another. To solve this problem he constructed several delay differential equations with damping described by . Despite the obvious importance in applications there are only few papers on delay .