The paper deals with qualitative aspects of the solutions of the nonlinear second-order Emden-Fowler equation
where is a positive real number, , , and . It is said that a solution of (E) is of nonlinear limit-circle type, if ; when the improper integral is equal to infinity the solution is said to be of nonlinear limit-point type. Moreover, if all solutions of (E) are of nonlinear limit-circle type then we say that (E) is of nonlinear limit-circle type, and (E) is of nonlinear limit-point type if there exists at least a solution being of nonlinear limit-point type.
Apart from distinguishing the cases or equal to , the authors impose some sufficient conditions on the coefficients and in order to ensure that (E) has nonlinear limit-circle or limit-point type. The results obtained are very involved for being described here. The authors apply their results to the examples (with and (with ). These examples are used to illustrate how the results obtained in this paper improve similar results contained in [M. Bartus̆ek, Z. Dos̆lá and J. R. Graef, The nonlinear limit-point/limit-circle problem.Boston, MA: Birkhäuser (2004; Zbl 1052.34021)].