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# Article

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Keywords:
half-linear equation; Riccati technique; variational principle; reciprocity principle; principal solution; oscillation and nonoscillation criteria
Summary:
In this paper we investigate oscillatory properties of the second order half-linear equation $(r(t)\Phi (y^{\prime }))^{\prime }+c(t)\Phi (y)=0, \quad \Phi (s):= |s|^{p-2}s. \qquad \mathrm{{(*)}}$ Using the Riccati technique, the variational method and the reciprocity principle we establish new oscillation and nonoscillation criteria for (*). We also offer alternative methods of proofs of some recent oscillation results.
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