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Section
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Mathematics
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Title
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On non-extensible solutions to second-order Emden-Fowler type differential equations with negative potential
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Author(-s)
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Korchemkina T.A.a
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Affiliations
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Lomonosov Moscow State Universitya
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Abstract
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Second-order Emden-Fowler type differential equations with regular nonlinearity and bounded negative potential depending on an independent variable, the solution and its first derivative are considered. The results on the existence of asymptotes of nontrivial solutions and estimates of the distance from the initial point to left and right asymptotes positions are given. Continuous dependence of the positions of left and right asymptotes of nontrivial solutions is obtained. The existence of a non-extensible solution with prescribed domain is proved.
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Keywords
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nonlinear differential equations, second-order, Emden-Fowler equations, continuous dependence of asymptote position, prescribed domain
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UDC
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517.925.44
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MSC
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34A99
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DOI
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10.20537/vm160209
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Received
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18 May 2016
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Language
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Russian
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Citation
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Korchemkina T.A. On non-extensible solutions to second-order Emden-Fowler type differential equations with negative potential, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2016, vol. 26, issue 2, pp. 231-238.
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References
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- Kondrat'ev V.A., Nikishkin V.A. On the positive solutions of the equation $y''=p(x)y$$k$ , Nekotorye voprosy kachestvennoi teorii differentsial'nykh uravnenii i teorii upravleniya dvizheniem (Some problems of the qualitative theory of differential equations and the theory of motion control), Saransk, 1980, pp. 131-141 (in Russian).
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- Dulina K.M., Korchemkina T.A. On existence of solutions to second-order Emden-Fowler type differential equations with prescribed domain, Proceedings of the International Conference “Qualitative theory of differential equations and applications”, Moscow State University of Economics, Statistics, and Informatics, 2014, pp. 19-27 (in Russian).
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