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Section
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Mathematics
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Title
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On asymptotic behaviour of solutions with infinite derivative for regular second-order Emden-Fowler type differential equations with negative potential
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Author(-s)
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Dulina K.M.a
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Affiliations
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Lomonosov Moscow State Universitya
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Abstract
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In this paper we consider the second-order Emden-Fowler type differential equation with negative potential $y''-p(x, y, y') |y|^k \text{ sgn } y=0$ in case of regular nonlinearity $k>1$. We assume that the function $p(x, u, v)$ is continuous in $x$ and Lipschitz continuous in two last variables. We investigate asymptotic behaviour of non-extensible solutions to the equation above. We consider the case of a positive function $p(x, u, v)$ unbounded from above and bounded away from 0 from below. The conditions guaranteeing an existence of a vertical asymptote of all nontrivial non-extensible solutions to the equation are obtained. Also the sufficient conditions providing the following solutions' properties $\displaystyle \lim_{x \to a} |y'(x)| = +\infty$, $\displaystyle \lim_{x \to a} |y(x)| <+ \infty$, where $a < \infty$ is a boundary point, are obtained.
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Keywords
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second-order Emden-Fowler type differential equations, regular nonlinearity, asymptotic behaviour
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UDC
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517.925.44
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MSC
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34C11, 34E10
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DOI
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10.20537/vm160206
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Received
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14 May 2016
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Language
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Russian
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Citation
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Dulina K.M. On asymptotic behaviour of solutions with infinite derivative for regular second-order Emden-Fowler type differential equations with negative potential, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2016, vol. 26, issue 2, pp. 207-214.
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References
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