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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, Number 12, Pages 3–10 (Mi ivm8849)  
This article is cited in 3 scientific papers (total in 3 papers)

A periodic boundary value problem for a fourth-order differential equation

A. R. Abdullaeva, E. A. Skachkovab

a Chair of Higher Mathematics, Perm National Research Polytechnic University, 29 Komsomol'skii Ave., Perm, 614990 Russia
b Chair of Mathematical Analysis, Perm State National Research University, 15 Bukirev str., Perm, 614990 Russia
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Abstract: In this paper we obtain sufficient solvability conditions for a periodic boundary value problem for a fourth-order ordinary differential equation. The research technique is based on the solvability theorem for a quasilinear operator equation in the case of resonance. We formulate sufficient conditions for the existence of periodic solutions in terms of the original equation. We show that the main result of this paper clarifies the existence theorem established by B. Mehry and D. Shadman in Sci. Iran. 15 (2), 182–185 (2008).
Keywords: fourth-order differential equation, periodic solution, resonance.
Received: 26.07.2012
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2013, Volume 57, Issue 12, Pages 1–7
DOI: https://doi.org/10.3103/S1066369X13120013
Bibliographic databases:
Document Type: Article
UDC: 517.927
Language: Russian
Citation: A. R. Abdullaev, E. A. Skachkova, “A periodic boundary value problem for a fourth-order differential equation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, no. 12, 3–10; Russian Math. (Iz. VUZ), 57:12 (2013), 1–7
Citation in format AMSBIB
\Bibitem{AbdSka13}
\by A.~R.~Abdullaev, E.~A.~Skachkova
\paper A periodic boundary value problem for a~fourth-order differential equation
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2013
\issue 12
\pages 3--10
\mathnet{http://mi.mathnet.ru/ivm8849}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2013
\vol 57
\issue 12
\pages 1--7
\crossref{https://doi.org/10.3103/S1066369X13120013}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84890511758}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
     
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