Geodesic
Weighted Hardy inequalities and their applications to oscillation theory of half-linear differential equations
Eurasian mathematical journal, Tome 1 (2010) no. 2, pp. 110-121

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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 $1$, we establish the properties of oscillation and nonoscillation. 
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R. Oinarov; S. Y. Rakhimova. Weighted Hardy inequalities and their applications to oscillation theory of half-linear differential equations. Eurasian mathematical journal, Tome 1 (2010) no. 2, pp. 110-121. http://geodesic.mathdoc.fr/item/EMJ_2010_1_2_a7/