Advances in Difference Equations
Volume 2010 (2010), Article ID 143298, 8 pages
doi:10.1155/2010/143298
On connection between second-order delay differential equations and integrodifferential equations with delay
Leonid Berezansky1
, Josef Diblík
and Zdenĕk Šmarda3
1Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
3Department of Mathematics, Faculty of Electrical Engineering and Communication, 61600, Brno University of Technology, Brno, Czech Republic
Abstract
The existence and uniqueness of solutions and a representation of solution formulas are studied for the following initial value problem: x˙(t)+∫t0tK(t,s)x(h(s))ds=f(t), t≥t0, x∈ℝn, x(t)=φ(t), t<t0. Such problems are obtained by transforming second-order delay differential equations x¨(t)+a(t)x˙(g(t))+b(t)x(h(t))=0 to first-order differential equations.