TY - JOUR

T1 - On connection between second-order delay differential equations and integrodifferential equations with delay

AU - Berezansky, Leonid

AU - Diblík, Josef

AU - Šmarda, Zdenk

PY - 2010/12/1

Y1 - 2010/12/1

N2 - The existence and uniqueness of solutions and a representation of solution formulas are studied for the following initial value problem: x (t) + t ∫0t K (t, s) x (h (s)) d s = f (t), t ≥ t 0, xε ℝn, x (t) = ω(t), t < t 0. 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.

AB - The existence and uniqueness of solutions and a representation of solution formulas are studied for the following initial value problem: x (t) + t ∫0t K (t, s) x (h (s)) d s = f (t), t ≥ t 0, xε ℝn, x (t) = ω(t), t < t 0. 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.

UR - http://www.scopus.com/inward/record.url?scp=78049291523&partnerID=8YFLogxK

U2 - 10.1186/1687-1847-2010-143298

DO - 10.1186/1687-1847-2010-143298

M3 - Article

AN - SCOPUS:78049291523

SN - 1687-1839

VL - 2010

JO - Advances in Difference Equations

JF - Advances in Difference Equations

M1 - 143298

ER -