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## Archive of Issues

Russia Moscow
Year
2016
Volume
26
Issue
2
Pages
231-238
 Section Mathematics Title On non-extensible solutions to second-order Emden-Fowler type differential equations with negative potential Author(-s) Korchemkina T.A.a Affiliations Lomonosov Moscow State Universitya Abstract 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. Keywords nonlinear differential equations, second-order, Emden-Fowler equations, continuous dependence of asymptote position, prescribed domain UDC 517.925.44 MSC 34A99 DOI 10.20537/vm160209 Received 18 May 2016 Language Russian Citation 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. References Kiguradze I.T., Chanturiya T.A. Asimptoticheskie svoistva reshenii neavtonomnykh obyknovennykh differentsial'nykh uravnenii (Asymptotic properties of solutions of nonautonomous ordinary differential equations), Moscow: Nauka, 1990, 432 p. Mitidieri E., Pohozhaev S.I. A priori estimates and blow-up of solutions to nonlinear partial differential equations and inequalities, Proceedings of the Steklov Institute of Mathematics, 2001, vol. 234, pp. 1-362. Astashova I. On quasi-periodic solutions to a higher-order Emden-Fowler type differential equation, Boundary Value Problems, 2014, Article ID 174, 8 p. Astashova I. Uniform estimates and existence of solutions with prescribed domain to nonlinear third-order differential equation, Differential and Difference Equations with Applications, Springer Proceedings in Mathematics and Statistics, New York: Springer, 2013, vol. 47, pp. 227-237. 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). 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). 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). Full text