Variation formulae for the solutions of delay differential equations with discontinuous initial conditions
Sbornik. Mathematics, Tome 196 (2005) no. 8, pp. 1137-1163
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Variation formulae are proved for solutions of non-linear differential equations with variable delays and discontinuous initial conditions. The discontinuity of the initial condition means that at the initial moment of time the values of the initial function and the trajectory, generally speaking, do not coincide. The formulae obtained contain a new summand connected with the discontinuity of the initial condition and the variation of the initial moment.
@article{SM_2005_196_8_a2,
author = {G. L. Kharatishvili and T. A. Tadumadze},
title = {Variation formulae for the solutions of delay differential equations with discontinuous initial conditions},
journal = {Sbornik. Mathematics},
pages = {1137--1163},
publisher = {mathdoc},
volume = {196},
number = {8},
year = {2005},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2005_196_8_a2/}
}
TY - JOUR AU - G. L. Kharatishvili AU - T. A. Tadumadze TI - Variation formulae for the solutions of delay differential equations with discontinuous initial conditions JO - Sbornik. Mathematics PY - 2005 SP - 1137 EP - 1163 VL - 196 IS - 8 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SM_2005_196_8_a2/ LA - en ID - SM_2005_196_8_a2 ER -
%0 Journal Article %A G. L. Kharatishvili %A T. A. Tadumadze %T Variation formulae for the solutions of delay differential equations with discontinuous initial conditions %J Sbornik. Mathematics %D 2005 %P 1137-1163 %V 196 %N 8 %I mathdoc %U http://geodesic.mathdoc.fr/item/SM_2005_196_8_a2/ %G en %F SM_2005_196_8_a2
G. L. Kharatishvili; T. A. Tadumadze. Variation formulae for the solutions of delay differential equations with discontinuous initial conditions. Sbornik. Mathematics, Tome 196 (2005) no. 8, pp. 1137-1163. http://geodesic.mathdoc.fr/item/SM_2005_196_8_a2/