Title:
|
Solvability conditions of the Cauchy problem for two-dimensional systems of linear functional differential equations with monotone operators (English) |
Author:
|
Šremr, Jiří |
Language:
|
English |
Journal:
|
Mathematica Bohemica |
ISSN:
|
0862-7959 (print) |
ISSN:
|
2464-7136 (online) |
Volume:
|
132 |
Issue:
|
3 |
Year:
|
2007 |
Pages:
|
263-295 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
We establish new efficient conditions sufficient for the unique solvability of the initial value problem for two-dimensional systems of linear functional differential equations with monotone operators. (English) |
Keyword:
|
system of functional differential equations with monotone operators |
Keyword:
|
initial value problem |
Keyword:
|
solvability |
MSC:
|
34C12 |
MSC:
|
34K05 |
MSC:
|
34K06 |
MSC:
|
34K10 |
idZBL:
|
Zbl 1174.34049 |
idMR:
|
MR2355659 |
DOI:
|
10.21136/MB.2007.134126 |
. |
Date available:
|
2009-09-24T22:31:48Z |
Last updated:
|
2020-07-29 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134126 |
. |
Reference:
|
[1] N. V. Azbelev, V. P. Maksimov, L. F. Rakhmatullina: Introduction to the Theory of Functional Differential Equations.Nauka, Moskva, 1991. (Russian) MR 1144998 |
Reference:
|
[2] N. Dilnaya, A. Rontó: Multistage iterations and solvability of linear Cauchy problems.Math. Notes (Miskolc) 4 (2003), 89–102. MR 2033998, 10.18514/MMN.2003.81 |
Reference:
|
[3] R. Hakl, E. Bravyi, A. Lomtatidze: Optimal conditions on unique solvability of the Cauchy problem for the first order linear functional differential equations.Czech. Math. J. 52 (2002), 513–530. MR 1923257, 10.1023/A:1021767411094 |
Reference:
|
[4] R. Hakl, A. Lomtatidze, B. Půža: New optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations.Math. Bohem. 127 (2002), 509–524. MR 1942637 |
Reference:
|
[5] R. Hakl, A. Lomtatidze, B. Půža: On a boundary value problem for first order scalar functional differential equations.Nonlinear Anal. 53 (2003), 391–405. MR 1964333, 10.1016/S0362-546X(02)00305-X |
Reference:
|
[6] R. Hakl, A. Lomtatidze, J. Šremr: Some Boundary Value Problems for First Order Scalar Functional Differential Equations.Folia Facultatis Scientiarum Naturalium Universitatis Masarykianae Brunensis, Brno, 2002. MR 2096135 |
Reference:
|
[7] R. Hakl, S. Mukhigulashvili: On a boundary value problem for $n$-th order linear functional differential systems.Georgian Math. J. 12 (2005), 229–236. MR 2174179 |
Reference:
|
[8] R. Hakl, J. Šremr: On the Cauchy problem for two-dimensional systems of linear functional differential equations with monotone operators.Nonlinear Oscil (to appear). MR 2394937 |
Reference:
|
[9] J. Hale: Theory of Functional Differential Equations.Springer, 1977. Zbl 0352.34001, MR 0508721 |
Reference:
|
[10] I. Kiguradze, B. Půža: Boundary Value Problems for Systems of Linear Functional Differential Equations.Folia Facultatis Scientiarum Naturalium Universitatis Masarykianae Brunensis, Brno, 2003. MR 2001509 |
Reference:
|
[11] I. Kiguradze, B. Půža: On boundary value problems for systems of linear functional differential equations.Czech. Math. J. 47 (1997), 341–373. 10.1023/A:1022829931363 |
Reference:
|
[12] V. Kolmanovskii, A. Myshkis: Introduction to the Theory and Applications of Functional Differential Equations.Kluwer Acad. Publ., Dordrecht, 1999. MR 1680144 |
Reference:
|
[13] A. Rontó: On the initial value problem for systems of linear differential equations with argument deviations.Math. Notes (Miskolc) 6 (2005), 105–127. Zbl 1079.34052, MR 2148846, 10.18514/MMN.2005.123 |
Reference:
|
[14] A. N. Ronto: Exact solvability conditions of the Cauchy problem for systems of linear first-order functional differential equations determined by $(\sigma _1,\sigma _2,\dots ,\sigma _n;\tau )$-positive operators.Ukrain. Mat. J. 55 (2003), 1853–1884. MR 2075708, 10.1023/B:UKMA.0000027047.61698.48 |
Reference:
|
[15] Š. Schwabik, M. Tvrdý, O. Vejvoda: Differential and Integral Equations: Boundary Value Problems and Adjoints.Academia, Praha, 1979. MR 0542283 |
Reference:
|
[16] J. Šremr: On the initial value problem for two-dimensional systems of linear functional differential equations with monotone operators.Fasc. Math. 37 (2007), 87–108. Zbl 1134.34038, MR 2320898 |
Reference:
|
[17] W. Walter: Differential and Integral Inequalities.Springer, 1970. Zbl 0252.35005, MR 0271508 |
. |