| Title:
|
On a two point linear boundary value problem for system of ODEs with deviating arguments (English) |
| Author:
|
Kubalčík, Jan |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
38 |
| Issue:
|
2 |
| Year:
|
2002 |
| Pages:
|
101-118 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Two point boundary value problem for the linear system of ordinary differential equations with deviating arguments \[{{x}^{\prime }(t) ={A}(t){x}(\tau _{11}(t))+{B}(t){u}(\tau _{12}(t)) +{q}_1(t)\,, {u}^{\prime }(t) ={C}(t){x}(\tau _{21}(t))+{D}(t){u}(\tau _{22}(t)) +{q}_2(t)\,, \alpha _{11} {x}(0) + \alpha _{12} {u}(0) = {c}_0, \quad \alpha _{21} {x}(T) + \alpha _{22} {u}(T) = {c}_T} \] is considered. For this problem the sufficient condition for existence and uniqueness of solution is obtained. The same approach as in [2], [3] is applied. (English) |
| Keyword:
|
existence and uniqueness of solution |
| Keyword:
|
two point linear boundary value problem |
| Keyword:
|
linear system of ordinary differential equations |
| Keyword:
|
deviating argument |
| Keyword:
|
delay |
| MSC:
|
34B05 |
| MSC:
|
34B10 |
| idZBL:
|
Zbl 1087.34044 |
| idMR:
|
MR1909592 |
| . |
| Date available:
|
2008-06-06T22:30:05Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107825 |
| . |
| Reference:
|
[1] Kiguradze, I., Půža, B.: On boundary value problems for systems of linear functional differential equations.Czechoslovak Math. J. 47 No. 2 (1997), 233–244. MR 1452425 |
| Reference:
|
[2] Kubalčík, J.: On a Two Point Boundary Value Problem for Linear System of ODEs.in press. |
| Reference:
|
[3] Kubalčík, J.: On one Two Point Boundary Value Problem for Linear System of ODEs with Deviating Arguments.CDDE 2000 Program, Abstract, Extended abstracts, Masaryk University, Brno 2000, 75–76. |
| Reference:
|
[4] Marshall, A. W., Olkin, I.: Inequalities: Theory of Majorization and Its Applications.Academic Press, 1979, (in Russian), Mir, Moskva, 1983. MR 0731533 |
| Reference:
|
[5] Kiguradze, I.: An initial value problem and boundary value problems for systems of ordinary differential equations. Vol.I: Linear theory.MU Brno 1997 (in Czech), Macniereba, Tbilisi 1997, 216pp. (in Russian). Zbl 0956.34505, MR 1484729 |
| Reference:
|
[6] Öztürk, I.: On the nonlocal boundary value problem for first order loaded differential equations.Indian J. Pure Appl. Math. 26, No. 4 (1995), 309–314. MR 1328759 |
| Reference:
|
[7] Jodar, L.: Boundary value problems and Green’s operator functions.Glas. Mat. Ser. III 24(44), No. 4 (1989), 511–522. Zbl 0712.34024, MR 1080079 |
| Reference:
|
[8] Jodar, L.: An algebraic approach for solving boundary value matrix problem: Existence, uniqueness and closed form solutions.Rev. Mat. Complut. 1, No. 1-3 (1988), 145–155. MR 0977046 |
| Reference:
|
[9] Kiguradze, I., Půža, B.: On the Vallée-Poussin problem for singular differential equations with deviating arguments.Arch. Math. (Brno) 33 No. 1-2 (1997), 127–138. MR 1464307 |
| Reference:
|
[10] Elsgolc, L. E., Norkin, S. B.: Introduction into theory of differential equations with deviating argument.Nauka Moskva 1971 (in Russian). MR 0352646 |
| Reference:
|
[11] Asmykovich, I. K., Marchenko, V. M.: Spectrum control in systems with delay.Avtom. Telemekh. No. 7, (1976), 5–14 (in Russian). MR 0444207 |
| Reference:
|
[12] Asmykovich, I. K., Marchenko, V. M.: Modal control of multiinput linear systems with delay.Avtom. Telemekh. No. 1 (1980), 5–10 (in Russian). |
| . |
