Geodesic
Asymptotic classification of solutions to the second-order Emden--Fowler type differential equation with negative potential
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 6 (2015), pp. 50-56

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Consider the second-order differential equation of Emden–Fowler type with negative potential $y'' - p\left(x, \, y,\, y'\right) |y|^k \, \mathrm{sgn} \, y = 0$. The function $p\left(x, \, y, \, y'\right)$ is assumed positive, continuous, and Lipschitz continuous in $y$, $y'.$ In the case of singular nonlinearity ($0$) the solutions to above equation can behave in 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 ($0$) are obtained.
Keywords: second-order ordinary differential equations, equations of Emden–Fowler type, maximally uniquely extended solutions, asymptotic classification, regular nonlinearity, singular nonlinearity.
Mots-clés : non-extensible solutions 
@article{VSGU_2015_6_a5,
     author = {K. M. Dulina and T. A. Korchemkina},
     title = {Asymptotic classification of solutions to the second-order {Emden--Fowler} type differential equation with negative potential},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {50--56},
     publisher = {mathdoc},
     number = {6},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2015_6_a5/}
}
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K. M. Dulina; T. A. Korchemkina. Asymptotic classification of solutions to the second-order Emden--Fowler type differential equation with negative potential. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 6 (2015), pp. 50-56. http://geodesic.mathdoc.fr/item/VSGU_2015_6_a5/