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Section Mathematics
Title Asymptotic behaviour of solutions to nonlinear differential equations with exponentially equivalent right-hand sides
Author(-s) Zabolotskiy S.A.a
Affiliations Lomonosov Moscow State Universitya
Abstract 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.
Keywords nonlinear ordinary differential equations, asymptotic equivalence
UDC 517.928.1
MSC 34C41, 34E10
DOI 10.20537/vm160207
Received 17 May 2016
Language Russian
Citation 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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