| Title:
|
General conditions guaranteeing the solvability of the Cauchy problem for functional differential equations (English) |
| Author:
|
Dilna, N. |
| Author:
|
Rontó, A. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
133 |
| Issue:
|
4 |
| Year:
|
2008 |
| Pages:
|
435-445 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
New general unique solvability conditions of the Cauchy problem for systems of general linear functional differential equations are established. The class of equations considered covers, in particular, linear equations with transformed argument, integro-differential equations, neutral type equations and their systems of an arbitrary order. (English) |
| Keyword:
|
functional differential equation |
| Keyword:
|
Cauchy problem |
| Keyword:
|
initial value problem |
| Keyword:
|
differential inequality |
| MSC:
|
34K06 |
| MSC:
|
34K10 |
| MSC:
|
35K05 |
| idZBL:
|
Zbl 1199.35131 |
| idMR:
|
MR2472490 |
| DOI:
|
10.21136/MB.2008.140631 |
| . |
| Date available:
|
2010-07-20T17:41:52Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140631 |
| . |
| Reference:
|
[1] Azbelev, N., Maksimov, V., Rakhmatullina, L.: Introduction to the Theory of Linear Functional Differential Equations.Advanced Series in Mathematical Science and Engineering, vol. 3, World Federation Publishers Company, Atlanta, GA (1995). Zbl 0867.34051, MR 1422013 |
| Reference:
|
[2] Azbelev, N. V., Rakhmatullina, L. F.: Theory of linear abstract functional-differential equations and applications.Mem. Differential Equations Math. Phys. 8 (1996), 1-102. Zbl 0870.34067, MR 1432626 |
| Reference:
|
[3] Hakl, R., Lomtatidze, A., Půža, B.: On a boundary value problem for first-order scalar functional differential equations.Nonlinear Anal. 53 (2003), 391-405. Zbl 1024.34056, MR 1964333, 10.1016/S0362-546X(02)00305-X |
| Reference:
|
[4] Hartman, P.: Ordinary Differential Equations.Classics in Applied Mathematics, vol. 38, Philadelphia, PA: SIAM, 2nd ed., unabridged, corrected republication of the 1982 original. ed. (2002). Zbl 1009.34001, MR 1929104 |
| Reference:
|
[5] Krasnoselskii, M. A.: Positive Solutions of Operator Equations.Wolters-Noordhoff Scientific Publications, Groningen (1964). MR 0181881 |
| Reference:
|
[6] Krasnoselskii, M. A., Lifshits, E. A., Pokornyi, Yu. V., Stetsenko, V. Ya.: Positively invertible linear operators and the solvability of non-linear equations.Russian Dokl. Akad. Nauk Tadzhik. SSR 17 (1974), 12-14. MR 0358427 |
| Reference:
|
[7] Krasnoselskii, M. A., Zabreiko, P. P.: Geometrical Methods of Nonlinear Analysis.Springer, Berlin (1984). MR 0736839 |
| Reference:
|
[8] Šremr, J.: On the Cauchy type problem for systems of functional differential equations.Nonlinear Anal. 67 3240-3260 (2007). Zbl 1130.34035, MR 2350882, 10.1016/j.na.2006.10.008 |
| . |
