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Title: A periodic boundary value problem in Hilbert space (English)
Author: Rudolf, Boris
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959
Volume: 119
Issue: 4
Year: 1994
Pages: 347-358
Summary lang: English
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Category: math
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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
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Date available: 2009-09-24T21:06:36Z
Last updated: 2015-09-04
Stable URL: http://hdl.handle.net/10338.dmlcz/126123
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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
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