Some Limit-point and Limit-circle Results for Second Order Emden–Fowler Equations

Abstract

The authors study the Emden–Fowler differential equation

where a(t)>0, r(t) > 0 , and λ ≠ 1 is positive. They consider both the case and the case and obtain some sufficient conditions for (E) to be of the nonlinear limit-circle type, sufficient conditions for it to be of the nonlinear limit-point type, and some necessary and sufficient conditions for equation (E) to be of the nonlinear limit-circle type.

Keywords:

• Nonlinear limit circle
• Nonlinear limit point
• Second order differential equations
• Emden–Flower equations
• AMS Subject Classifications: Primary 34B20
• 34C10
• 34C15
• 34D05