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This article is cited in 1 scientific paper (total in 1 paper)
MATHEMATICS
Asymptotic behaviour of solutions to nonlinear differential equations with exponentially equivalent right-hand sides
S. A. Zabolotskiy Lomonosov Moscow State University, Leninskie Gory, 1, Moscow, 119991, Russia
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.
Received: 17.05.2016
Citation:
S. A. Zabolotskiy, “Asymptotic behaviour of solutions to nonlinear differential equations with exponentially equivalent right-hand sides”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 26:2 (2016), 215–220
Linking options:
https://www.mathnet.ru/eng/vuu532 https://www.mathnet.ru/eng/vuu/v26/i2/p215
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Abstract page: | 337 | Full-text PDF : | 190 | References: | 57 |
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