Asymptotic classification of solutionsto the second-order Emden - Fowler type differential equation with negativepotential
- Authors: Dulina K.1, Korchemkina T.1
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Affiliations:
- Lomonosov Moscow State University
- Issue: Vol 21, No 6 (2015)
- Pages: 50-56
- Section: Articles
- URL: https://journals.ssau.ru/est/article/view/4467
- DOI: https://doi.org/10.18287/2541-7525-2015-21-6-50-56
- ID: 4467
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Abstract
Consider the second-order differential equation of Emden - Fowler type with negative potential y′′ - p (x, y, y′) |y|sgn y = 0: The function p (x; y; y′) is assumed positive, continuous, and Lipschitz continuous in y, y′: In the case ofsingular nonlinearity (0 < k < 1) the solutions to above equation can behavein a special way not only near the boundaries of their domains but also near internal points of the domains. This is why a notion of maximally uniquely extended solutions is introduced. Asymptotic classification of non-extensible solutions to above equation in case of regular nonlinearity (k > 1) and classification of maximally uniquely extended solutions to above equation in case of singular nonlinearity (0 < k < 1) are obtained.
About the authors
K.M. Dulina
Lomonosov Moscow State University
Author for correspondence.
Email: morenov.sv@ssau.ru
T.A. Korchemkina
Lomonosov Moscow State University
Email: morenov.sv@ssau.ru