Geodesic
An oscillatory half-linear differential equation
Archivum mathematicum, Tome 33 (1997) no. 4, pp. 355-361

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A second-order half-linear ordinary differential equation of the type $$(|y^{\prime}|^{\alpha-1}y^{\prime})^{\prime}+\alpha q(t)|y|^{\alpha-1}y=0 \leqno{{\rm (1)}}$$ 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.
Classification : 34C10, 35J60, 46F10
Keywords: half-linear differential equations 
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     title = {An oscillatory half-linear differential equation},
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Elbert, Árpád; Kusano, Takaŝi; Tanigawa, Tomoyuki. An oscillatory half-linear differential equation. Archivum mathematicum, Tome 33 (1997) no. 4, pp. 355-361. http://geodesic.mathdoc.fr/item/ARM_1997__33_4_a9/