A periodic boundary value problem in Hilbert space

Boris Rudolf

Mathematica Bohemica (1994)

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

Abstract

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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.

How to cite

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Rudolf, 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

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  1. K. Deimling, Ordinary differential equations in Banach spaces, Springer-Verlag, Berlin-Heidelberg-New York, 1977. (1977) Zbl0361.34050MR0463601
  2. M. Greguš M. Švec V. Šeda, Ordinary differential equations, Alfa, Bratislava, 1985. (In Slovak.) (1985) 
  3. Chaitan P. Gupta, Boundary value problems for differential equations in Hilbert spaces involving reflection of the argument, JMAA 128 (1987), 375-388. (1987) MR0917372
  4. J. Mawhin, 10.2748/tmj/1178229639, Tohoku Math. J. 32 (1980), 225-233. (1980) Zbl0436.34057MR0580278DOI10.2748/tmj/1178229639
  5. 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
  6. 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
  7. E. Zeidler, Functional analysis and its applications I, Springer-Verlag, 1986. (1986) Zbl0583.47050MR0816732

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