Optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations

@article{Bravyi2002,
abstract = {Nonimprovable, in a sense sufficient conditions guaranteeing the unique solvability of the problem \[ u^\{\prime \}(t)=\ell (u)(t)+q(t), \qquad u(a)=c, \] where $\ell \:C(I,\mathbb \{R\})\rightarrow L(I,\mathbb \{R\})$ is a linear bounded operator, $q\in L(I,\mathbb \{R\})$, and $c\in \mathbb \{R\}$, are established.},
author = {Bravyi, E., Hakl, Robert, Lomtatidze, Alexander},
journal = {Czechoslovak Mathematical Journal},
keywords = {linear functional differential equations; Cauchy problem; existence and uniqueness; differential inequalities; linear functional-differential equations; Cauchy problem; existence and uniqueness; differential inequalities},
language = {eng},
number = {3},
pages = {513-530},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations},
url = {http://eudml.org/doc/30720},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Bravyi, E.
AU - Hakl, Robert
AU - Lomtatidze, Alexander
TI - Optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations
JO - Czechoslovak Mathematical Journal
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 3
SP - 513
EP - 530
AB - Nonimprovable, in a sense sufficient conditions guaranteeing the unique solvability of the problem \[ u^{\prime }(t)=\ell (u)(t)+q(t), \qquad u(a)=c, \] where $\ell \:C(I,\mathbb {R})\rightarrow L(I,\mathbb {R})$ is a linear bounded operator, $q\in L(I,\mathbb {R})$, and $c\in \mathbb {R}$, are established.
LA - eng
KW - linear functional differential equations; Cauchy problem; existence and uniqueness; differential inequalities; linear functional-differential equations; Cauchy problem; existence and uniqueness; differential inequalities
UR - http://eudml.org/doc/30720
ER -