Tatiana Korchemkina
abstract:
The second-order differential equation with general power-law nonlinearity with
continuous potential bounded by positive constants is considered. The behavior
of solutions to the equation is studied with respect to the values of
nonlinearity. The necessary and sufficient conditions for the existence of a
finite right-side boundary of the domain or horizontal asymptote are obtained.
The distance to the right-side boundary of the domain and the limits of
solutions with horizontal asymptotes near their boundaries are estimated. The
continuous dependence of the right-side boundary of the domain and horizontal
asymptotes on initial data is proved.
Mathematics Subject Classification: 34C11, 34C99
Key words and phrases: Second-order differential equations, nonlinear differential equations, power-law nonlinearity, vertical asymptote, horizontal asymptote, black hole solution, white hole solution, uniform estimates, continuous dependence