A perturbed second order nonlinear equation
is defined to be of the limit circle type if, for any solution x(t), either
(this is a generalization of H. Weyl
’s [Math. Ann. 68, 220-269 (1910)] classification of second order linear differential equations
. The authors give sufficient conditions that such equations are of the limit circle type. Moreover, they discuss the relationships between the above property and the boundedness, oscillation and convergence to zero of the solution of the above equation.