This article is cited in 1 paper

MATHEMATICS

On non-extensible solutions to second-order Emden–Fowler type differential equations with negative potential

T. A. Korchemkina

Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Leninskie Gory, 1, GSP-1, Moscow, 119991, Russia

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

Received: 18.05.2016

DOI: 10.20537/vm160209

Bibliographic databases:

• 
•