Open AccessAsymptotic classification of solutionsto the second-order Emden - Fowler type differential equation with negativepotential
Author(s) -
K. Dulina,
T. A. Korchemkina
Publication year - 2015
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2015-21-6-50-56
Subject(s) - lipschitz continuity , mathematics , type (biology) , order (exchange) , nonlinear system , function (biology) , mathematical analysis , pure mathematics , physics , quantum mechanics , ecology , finance , economics , evolutionary biology , biology
Consider the second-order dierential 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.