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Methods of oscillation theory of half-linear second order differential equations

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Abstract

In this paper we investigate oscillatory properties of the second order half-linear equation

$$\left( * \right){\text{ }}\left( {r\left( t \right)\Phi \left( {y\prime } \right)} \right)\prime + c\left( t \right)\Phi \left( y \right) = 0,{\text{ }}\Phi \left( s \right): = \left| s \right|^{p - 2} s.$$

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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Došlý, O. Methods of oscillation theory of half-linear second order differential equations. Czechoslovak Mathematical Journal 50, 657–671 (2000). https://doi.org/10.1023/A:1022854131381

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