Positive solutions to a class of second order differential equations with singular nonlinearities

Abstract

A class of second order quasilinear differential equations with singular nonlinearities is considered. The set of all possible solutions defined on a positive half-line [a,∞) is classified into six types according to their aymptotic behavior as t→∞, and sharp conditions are established for the existence of solutions belonging to each of the classified types.

Keywords:

• Quasilinear differential equation
• Singular nonlinearity
• positive solution
• asymptotic behavior