Geodesic
Conditional oscillation of half-linear differential equations with periodic coefficients
Archivum mathematicum, Tome 44 (2008) no. 2, pp. 119-131.

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We show that the half-linear differential equation \[ \big [r(t)\Phi (x^{\prime })\big ]^{\prime } + \frac{s(t)}{t^p} \Phi (x) = 0 \ast \] with $\alpha $-periodic positive functions $r, s$ is conditionally oscillatory, i.e., there exists a constant $K>0$ such that () with $\frac{\gamma s(t)}{t^p}$ instead of $\frac{s(t)}{t^p}$ is oscillatory for $\gamma > K$ and nonoscillatory for $\gamma K$.
Classification : 34C10
Keywords: oscillation theory; conditional oscillation; half-linear differential equations 
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     author = {Hasil, Petr},
     title = {Conditional oscillation of half-linear differential equations with periodic coefficients},
     journal = {Archivum mathematicum},
     pages = {119--131},
     publisher = {mathdoc},
     volume = {44},
     number = {2},
     year = {2008},
     mrnumber = {2432849},
     zbl = {1212.34110},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2008__44_2_a4/}
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Hasil, Petr. Conditional oscillation of half-linear differential equations with periodic coefficients. Archivum mathematicum, Tome 44 (2008) no. 2, pp. 119-131. http://geodesic.mathdoc.fr/item/ARM_2008__44_2_a4/