Asymptotic classification of solutionsto the second-order Emden - Fowler type differential equation with negativepotential

Cite item


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.

T.A. Korchemkina

Lomonosov Moscow State University



Copyright (c) 2017 К.М. Дулина, Т.А. Корчемкина

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies