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Criteria for oscillatory behavior of solutions of fourth order half-linear differential equations of the form $$\left(\right|y^{\text{'}\text{'}}{|}^{\alpha }\mathrm{sgn}{y}^{\text{'}\text{'}}{)}^{\text{'}\text{'}}+q\left(t\right){\left|y\right|}^{\alpha }\mathrm{sgn}y=0,t\ge a>0,A$$ where $\alpha >0$ is a constant and $q\left(t\right)$ is positive continuous function on $[a,\infty )$, are given in terms of an increasing continuously differentiable function $\omega \left(t\right)$ from $[a,\infty )$ to $(0,\infty )$ which satisfies ${\int }_a^{\infty }1/\left(t\omega \left(t\right)\right)dt<\infty$.

A second-order half-linear ordinary differential equation of the type $$\left(\right|y^{\text{'}}{|}^{\alpha -1}{y}^{\text{'}}{)}^{\text{'}}+\alpha q\left(t\right){\left|y\right|}^{\alpha -1}y=0\left(1\right)$$ is considered on an unbounded interval. A simple oscillation condition for (1) is given in such a way that an explicit asymptotic formula for the distribution of zeros of its solutions can also be established.