On the Limit-point / Limit-circle Problem for Second Order Nonlinear Equations

Abstract

The authors study the nonlinear limit-point / limit-circle problem for the second order differential equation $$y'' = r(t)f(y)$$ where $r(t)\geq 0$ and $xf(x) > 0$ for $x\neq 0$. Examples are included to show that some of the hypotheses are quite sharp.