Weighted Hardy inequalities and their applications to oscillation theory of half-linear differential equations

For the equation
$$ \left(\rho(t)|y'(t)|^{p-2}y'(t)\right)'+v(t)|y(t)|^{p-2}y(t)=0,\quad t\in (a,b) $$
where $1<p<\infty$, we establish the properties of oscillation and nonoscillation.