Distance between vertical asymptotes of solutions of certain nonlinear differential equations

In [S.B. Eliason, On the distance between vertical asymptotes of solutions of a second-order differential equation, J. Math. Anal. Appl. 35 (1971) 148–156], Eliason asks the question if there are results concerning bounds for the distance between vertical asymptotes of solutions of the second-order differential equation (ry′)′−pyf(y)=0(ry′)′−pyf(y)=0, in the case where the solution yy has at least one zero between each consecutive pair of its vertical asymptotes. In this paper, we answer in the affirmative by presenting such results. We also present other related results for some other nonlinear differential equations.