Section
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Mathematics
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Title
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Asymptotic behaviour of solutions to nonlinear differential equations with exponentially equivalent right-hand sides
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Author(-s)
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Zabolotskiy S.A.a
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Affiliations
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Lomonosov Moscow State Universitya
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Abstract
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Nonlinear $n$-th order differential equations with lower term are considered. With the help of the contraction mapping principle an asymptotic equivalence of solutions to these equations is investigated in the case of exponentially equivalent right-hand sides. Obtained sufficient conditions for asymptotic equivalence of solutions extend and generalize results stated in previous author’s papers. The result, describing the asymptotic behaviour of all tending to zero at infinity solutions to second order differential equations with regular Emden-Fowler type nonlinearity and zero right-hand side appearing while investigating quasilinear elliptic equations, is stated. On the basis of this result the asymptotic behaviour of solutions to a corresponding equation with nonzero right-hand side is described.
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Keywords
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nonlinear ordinary differential equations, asymptotic equivalence
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UDC
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517.928.1
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MSC
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34C41, 34E10
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DOI
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10.20537/vm160207
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Received
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17 May 2016
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Language
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Russian
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Citation
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Zabolotskiy S.A. Asymptotic behaviour of solutions to nonlinear differential equations with exponentially equivalent right-hand sides, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2016, vol. 26, issue 2, pp. 215-220.
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References
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- Astashova I.V. Qualitative properties of solutions to quasilinear ordinary differential equations, Kachestvennye svoistva reshenii differentsial'nykh uravnenii i smezhnye voprosy spektral'nogo analiza (Qualitative properties of solutions to differential equations and related topics of spectral analysis), Moscow: Unity-Dana, 2012, pp. 22-288 (in Russian).
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