Section
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Mathematics
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Title
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On unimprovable conditions of the solvability of the periodic problem for second order functional differential equations
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Author(-s)
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Bravyi E.I.a
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Affiliations
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Perm National Research Polytechnical Universitya
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Abstract
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Necessary and sufficient conditions for the unique solvability of the periodic boundary value problem for all linear second order functional differential equations with the given norm of the functional operators.
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Keywords
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linear equations with delay, periodic boundary value problem, periodic solutions, functional differential equations
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UDC
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517.917
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MSC
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34K06, 34K10, 34K13
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DOI
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10.20537/vm130301
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Received
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15 June 2013
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Language
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Russian
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Citation
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Bravyi E.I. On unimprovable conditions of the solvability of the periodic problem for second order functional differential equations, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2013, issue 3, pp. 3-19.
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References
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- Lasota A., Opial Z. Sur les solutions periodiques des equations differentielles ordinaires, Ann. Polon. Math., 1964, vol. 16, no. 1, pp. 69-94.
- Komlenko Yu.V., Tonkov E.L. The periodic boundary value problem for a second order ordinary differential equation, Dokl. Akad. Nauk SSSR, 1968, vol. 179, no. 1, pp. 17-19.
- Cabada A., Cid J.A. On the sign of the Green's function associated to Hill's equation with an indefinite potential, Appl. Math. Comput., 2008, vol. 205, no. 1, pp. 303-308.
- Hakl R., Torres P.J. Maximum and antimaximum principles for a second order differential operator with variable coefficients of indefinite sign, Appl. Math. Comput., 2011, vol. 217, no. 19, pp. 7599-7611.
- Lomtatidze A., Mukhigulashvili S. On periodic solutions of second order functional differential equations, Mem. Differential Equations Math. Phys., 1995, vol. 5, pp. 125-126.
- Azbelev N.V., Maksimov V.P., Rakhmatullina L.F. Vvedenie v teoriyu funktsional'no-differentsial'nykh uravnenii (Introduction to the theory of functional differential equations), Мoscow: Nauka, 1991, 280 p.
- Hakl R., Mukhigulashvili S. A periodic boundary value problem for functional differential equations of higher order, Georgian Math. J., 2009, vol. 16, no. 4, pp. 651-665.
- Bravyi E.I. On the best constants in the solvability conditions for the periodic boundary value problem for higher-order functional differential equations, Differ. Uravn., 2012, vol. 48, no. 6, pp. 773-780.
- Bravyi E.I. Razreshimost' kraevykh zadach dlya lineinykh funktsional'no-differentsial'nykh uravnenii (The solvability of boundary value problems for linear functional differential equations), Moscow-Izhevsk: Regular & Chaotic Dynamics, 2011, 372 p.
- Bravyi E.I. On the solvability of the periodic boundary value problem for a linear functional differential equation, Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2009, no. 3, pp. 12-24.
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Full text
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