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


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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

References


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

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