ASYMPTOTIC BEHAVIOR OF UNBOUNDED SOLUTIONS OF SECOND-ORDER DIFFERENTIAL EQUATIONS WITH GENERAL NONLINEARITIES

摘要

One considers second-order ordinary differential equations with general nonlinearities and a bounded potential. Depending on the type of nonlinearity, qualitative behavior of solutions is described. For solutions that are unbounded near the boundaries of their domain, asymptotic formulas are obtained in the case of equations with constant or variable potentials.