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 -