Geodesic
Optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations
Czechoslovak Mathematical Journal, Tome 52 (2002) no. 3, pp. 513-530 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 34K06, 34K10
Keywords: linear functional differential equations; Cauchy problem; existence and uniqueness; differential inequalities 
@article{CMJ_2002_52_3_a5,
     author = {Bravyi, E. and Hakl, R. and Lomtatidze, A.},
     title = {Optimal conditions for unique solvability of the {Cauchy} problem for first order linear functional differential equations},
     journal = {Czechoslovak Mathematical Journal},
     pages = {513--530},
     year = {2002},
     volume = {52},
     number = {3},
     mrnumber = {1923257},
     zbl = {1023.34055},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2002_52_3_a5/}
}
TY  - JOUR
AU  - Bravyi, E.
AU  - Hakl, R.
AU  - Lomtatidze, A.
TI  - Optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations
JO  - Czechoslovak Mathematical Journal
PY  - 2002
SP  - 513
EP  - 530
VL  - 52
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/CMJ_2002_52_3_a5/
LA  - en
ID  - CMJ_2002_52_3_a5
ER  - 
%0 Journal Article
%A Bravyi, E.
%A Hakl, R.
%A Lomtatidze, A.
%T Optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations
%J Czechoslovak Mathematical Journal
%D 2002
%P 513-530
%V 52
%N 3
%U http://geodesic.mathdoc.fr/item/CMJ_2002_52_3_a5/
%G en
%F CMJ_2002_52_3_a5
Bravyi, E.; Hakl, R.; Lomtatidze, A. Optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations. Czechoslovak Mathematical Journal, Tome 52 (2002) no. 3, pp. 513-530. http://geodesic.mathdoc.fr/item/CMJ_2002_52_3_a5/

[1] N. V.  Azbelev, V. P.  Maksimov and L. F.  Rakhmatullina: Introduction to the Theory of Functional Differential Equations. Nauka, Moscow, 1991. (Russian) | MR

[2] Sh.  Gelashvili and I.  Kiguradze: On multi-point boundary value problems for systems of functional differential and difference equations. Mem. Differential Equations Math. Phys. 5 (1995), 1–113. | MR

[3] P.  Hartman: Ordinary Differential Equations. John Wiley, New York, 1964. | MR | Zbl

[4] I.  Kiguradze and B.  Půža: On boundary value problems for systems of linear functional differential equations. Czechoslovak Math. J. 47 (1997), 341–373. | DOI | MR

[5] Š.  Schwabik, M.  Tvrdý and O.  Vejvoda: Differential and integral equations: boundary value problems and adjoints. Academia, Praha, 1979. | MR