Disconjugate operators and related differential equations

There are studied asymptotic properties of solutions of the nonlinear differential equation $L_nx+ p(t)f(x)=0$, where $L_n$ is disconjugate operator, $p$ is of one sign and $f(u)u>0$ for $u\ne 0$. Some comparison theorems in terms of property A and property B between linear and nonlinear equations are also given which generalize known results for $n=3$.