Abstract: | Some necessary and sufficient conditions for nonoscillation are established for the second order nonlinear differential equation
(r(t)y(x(t))|x¢(t)|p-1x¢(t))¢+c(t)f(x(t))=0, t 3 t0,(r(t)\psi(x(t))\vert x^{\prime}(t)\vert^{p-1}x^{\prime}(t))^{\prime}+c(t)f(x(t))=0,\quad t\ge t_0, |