| Title:
|
A periodic boundary value problem in Hilbert space (English) |
| Author:
|
Rudolf, Boris |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
119 |
| Issue:
|
4 |
| Year:
|
1994 |
| Pages:
|
347-358 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the paper some existence results for periodic boundary value problems for the ordinary differential equation of the second order in a Hilbert space are given. Under some auxiliary assumptions the set of solutions is compact and connected or it is convex. (English) |
| Keyword:
|
Leray-Schauder theorem |
| Keyword:
|
periodic boundary value problem |
| Keyword:
|
existence |
| Keyword:
|
uniqueness |
| Keyword:
|
periodic solutions |
| Keyword:
|
convexity of set of solutions |
| MSC:
|
34B15 |
| MSC:
|
34C25 |
| MSC:
|
34G20 |
| MSC:
|
47H15 |
| MSC:
|
47N20 |
| idZBL:
|
Zbl 0815.34059 |
| idMR:
|
MR1316586 |
| DOI:
|
10.21136/MB.1994.126123 |
| . |
| Date available:
|
2009-09-24T21:06:36Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126123 |
| . |
| Reference:
|
[D] K. Deimling: Ordinary differential equations in Banach spaces.Springer-Verlag, Berlin-Heidelberg-New York, 1977. Zbl 0361.34050, MR 0463601 |
| Reference:
|
[GŠŠ] M. Greguš M. Švec V. Šeda: Ordinary differential equations.Alfa, Bratislava, 1985. (In Slovak.) |
| Reference:
|
[G] Chaitan P. Gupta: Boundary value problems for differential equations in Hilbert spaces involving reflection of the argument.JMAA 128 (1987), 375-388. MR 0917372 |
| Reference:
|
[M] J. Mawhin: Two point boundary value problems for nonlinear second order differential equations in Hilbert spaces.Tohoku Math. J. 32 (1980), 225-233. Zbl 0436.34057, MR 0580278, 10.2748/tmj/1178229639 |
| Reference:
|
[R] B. Rudolf: Periodic boundary value problem in Hilbert space for differential equation of second order with reflection of the argument.Mathematica Slovaca 42 (1992), 65-84. Zbl 0744.34062, MR 1159492 |
| Reference:
|
[ST] K. Schmitt R. Thompson: Boundary value problems for infinite systems of second-order differential equations.J. Differential Equations 18 (1975), 277-295. MR 0374594, 10.1016/0022-0396(75)90063-7 |
| Reference:
|
[Z] E. Zeidler: Functional analysis and its applications I.Springer-Verlag, 1986. Zbl 0583.47050, MR 0816732 |
| . |
