| Title:
|
On one-sided estimates for row-finite systems of ordinary differential equations (English) |
| Author:
|
Herzog, Gerd |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
124 |
| Issue:
|
1 |
| Year:
|
1999 |
| Pages:
|
67-76 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove an existence and uniqueness theorem for row-finite initial value problems. The right-hand side of the differential equation is supposed to satisfy a one-sided matrix Lipschitz condition with a quasimonotone row-finite matrix which has an at most countable spectrum. (English) |
| Keyword:
|
Fréchet spaces |
| Keyword:
|
row-finite systems |
| Keyword:
|
one-sided estimates |
| Keyword:
|
row-finite matrices |
| MSC:
|
34A12 |
| MSC:
|
34G20 |
| idZBL:
|
Zbl 0937.34004 |
| idMR:
|
MR1687421 |
| DOI:
|
10.21136/MB.1999.125972 |
| . |
| Date available:
|
2009-09-24T21:35:08Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125972 |
| . |
| Reference:
|
[1] Bogachev V. I.: Deterministic and stochastic differential equations in infinite dimensional spaces.Acta Appl. Math. 40 (1995), 25-93. Zbl 0829.34050, MR 1338443, 10.1007/BF01518365 |
| Reference:
|
[2] Deimling K.: Ordinary Differential Equations in Banach Spaces.Lecture Notes in Mathematics 596, Springer, 1977. Zbl 0361.34050, MR 0463601, 10.1007/BFb0091643 |
| Reference:
|
[3] Feldstein A., Iserles A., Levin D.: Embedding of delay equations into an infinite-dimensional ODE system.J. Differential Equations 117(1995), 127-150. Zbl 0817.34045, MR 1320185, 10.1006/jdeq.1995.1050 |
| Reference:
|
[4] Herzog G.: Über gewöhnliche Differentialgleichungen in Fréchetraumen.Dissertation, Univ. Karlsruhe, 1992. |
| Reference:
|
[5] Herzog G.: On ordinary linear differential equations in $C^J$.Demonstratio Math. 28 (1995), 383-398. MR 1346844 |
| Reference:
|
[6] Herzog G.: On linear time-dependent row-finite systems of differential equations.Travaux Math. Sem. Math. Luxemb. 8 (1996), 167-176. Zbl 0978.34042, MR 1476744 |
| Reference:
|
[7] Herzog G.: On existence and uniqueness conditions for ordinary differential equations in Fréchet spaces.Studia Sci. Math. Hungar. 23 (1996), 367-375. Zbl 0880.34066, MR 1432178 |
| Reference:
|
[8] Herzog G.: One-sided estimates for ordinary differential equations in Fréchet spaces.Ricerche Mat. 46 (1997), 479-487. Zbl 0947.34048, MR 1760389 |
| Reference:
|
[9] Kaplansky I.: Infinite Abelian Groups.The University of Michigan Press, 4th printing, 1962. MR 0065561 |
| Reference:
|
[10] Körber K.H.: Das Spektrum zeilenfiniter Matrizen.Math. Ann. 181 (1969), 8-34. MR 0262863, 10.1007/BF01351175 |
| Reference:
|
[11] Lemmert R., Weckbach Ä.: Charakterisierungen zeilenendlicher Matrizen mit abzählbarem Spektrum.Math. Z. 188 (1984), 119-124. Zbl 0554.47015, MR 0767369, 10.1007/BF01163880 |
| Reference:
|
[12] Lemmert R.: On ordinary differential equations in locally convex spaces.Nonlinear Analysis 10 (1986), 1385-1390. Zbl 0612.34056, MR 0869547, 10.1016/0362-546X(86)90109-4 |
| Reference:
|
[13] Lobanov S. G., Smolyanov O. G.: Ordinary differential equations in locally convex spaces.Russ. Math. Surv. 49 (1994), 97-175. Zbl 0834.34076, MR 1289388, 10.1070/RM1994v049n03ABEH002258 |
| Reference:
|
[14] Martin R. H.: Nonlinear Operators and Differential Equations in Banach Spaces.Robert E. Krieger Publishing Company, Malabar, Florida, 1987. MR 0887947 |
| Reference:
|
[15] Moszyński K., Pokrzywa A.: Sur les systèmes infinis d'équations différentielles ordinaires dans certains espaces de Fréchet.Dissertationes Math. 115 (1974), 1-37. Zbl 0291.34049, MR 0390415 |
| Reference:
|
[16] Polewczak J.: Ordinary differential equations on closed subsets of Fréchet spaces with applications to fixed point theorems.Proc. Amer. Math. Soc. 107 (1989), 1005-1012. Zbl 0684.34062, MR 1019755 |
| Reference:
|
[17] Polewczak J.: Ordinary differential equations on closed subsets of locally convex spaces with applications to fixed point theorems.J. Math. Anal. Appl. 151 (1990), 208-225. Zbl 0721.34074, MR 1069457, 10.1016/0022-247X(90)90252-B |
| Reference:
|
[18] Schmidt S.: Existenzsätze für gewöhnliche Differentialgleichungen in Banachräumen.Funkcial. Ekvac. 35 (1992), 199-222. Zbl 0785.34045, MR 1189893 |
| Reference:
|
[19] Tychonov A.N.: Ein Fixpunktsatz.Math. Ann. 111 (1935), 767-776. MR 1513031 |
| Reference:
|
[20] Vim H.: Elementarteilertheorie unendlicher Matrizen.Math. Ann. 114 (1937), 493-505. MR 1513152, 10.1007/BF01594190 |
| Reference:
|
[21] Volkmann P.: Ein Existenzsatz für gewöhnliche Differentialgleichungen in Banachräumen.Proc. Amer. Math. Soc. 80 (1980), 297-300. Zbl 0506.34051, MR 0577763 |
| Reference:
|
[22] Wagner E.: Über ein abzählbares System gewöhnlicher linearer Differentialgleichungen von Bandstruktur.Demonstratio Math. 23 (1990), 753-773. Zbl 0734.34016, MR 1101540 |
| Reference:
|
[23] Williamson J. H.: Spectral representation of linear transformations in $\omega$.Proc. Cambridge Philos. Soc. 41 (1951), 461-472. Zbl 0042.12201, MR 0042615 |
| . |
