On the oscillation and nonoscillation of second order sublinear equations

Abstract:

An oscillation criterion and a nonoscillation criterion are given for the sublinear equation $y'' + a(t)|y{|^\gamma }\operatorname {sgn} y = 0$, $0 < \gamma < 1,t \in [0,\infty )$, where $a(t)$ is allowed to change sign. When applied to the special case $a(t) = {t^\lambda }\sin t$, we deduce oscillation for $\lambda > - \gamma$ and nonoscillation for $\lambda < - \gamma$.