# A periodic boundary value problem in Hilbert space

Mathematica Bohemica (1994)

- Volume: 119, Issue: 4, page 347-358
- ISSN: 0862-7959

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topRudolf, Boris. "A periodic boundary value problem in Hilbert space." Mathematica Bohemica 119.4 (1994): 347-358. <http://eudml.org/doc/29277>.

@article{Rudolf1994,

abstract = {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.},

author = {Rudolf, Boris},

journal = {Mathematica Bohemica},

keywords = {Leray-Schauder theorem; periodic boundary value problem; existence; uniqueness; periodic solutions; convexity of set of solutions; Leray-Schauder theorem; periodic boundary value problem; existence; uniqueness; periodic solutions},

language = {eng},

number = {4},

pages = {347-358},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {A periodic boundary value problem in Hilbert space},

url = {http://eudml.org/doc/29277},

volume = {119},

year = {1994},

}

TY - JOUR

AU - Rudolf, Boris

TI - A periodic boundary value problem in Hilbert space

JO - Mathematica Bohemica

PY - 1994

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 119

IS - 4

SP - 347

EP - 358

AB - 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.

LA - eng

KW - Leray-Schauder theorem; periodic boundary value problem; existence; uniqueness; periodic solutions; convexity of set of solutions; Leray-Schauder theorem; periodic boundary value problem; existence; uniqueness; periodic solutions

UR - http://eudml.org/doc/29277

ER -

## References

top- K. Deimling, Ordinary differential equations in Banach spaces, Springer-Verlag, Berlin-Heidelberg-New York, 1977. (1977) Zbl0361.34050MR0463601
- M. Greguš M. Švec V. Šeda, Ordinary differential equations, Alfa, Bratislava, 1985. (In Slovak.) (1985)
- Chaitan P. Gupta, Boundary value problems for differential equations in Hilbert spaces involving reflection of the argument, JMAA 128 (1987), 375-388. (1987) MR0917372
- J. Mawhin, 10.2748/tmj/1178229639, Tohoku Math. J. 32 (1980), 225-233. (1980) Zbl0436.34057MR0580278DOI10.2748/tmj/1178229639
- 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. (1992) Zbl0744.34062MR1159492
- K. Schmitt R. Thompson, 10.1016/0022-0396(75)90063-7, J. Differential Equations 18 (1975), 277-295. (1975) MR0374594DOI10.1016/0022-0396(75)90063-7
- E. Zeidler, Functional analysis and its applications I, Springer-Verlag, 1986. (1986) Zbl0583.47050MR0816732

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