Qualitative theory of half-linear second order differential equations

Ondřej Došlý

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Qualitative theory of half-linear second order differential equations

Došlý, Ondřej

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

Ondřej Došlý (2000)

Czechoslovak Mathematical Journal

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In this paper we investigate oscillatory properties of the second order half-linear equation ${(r (t) Φ (y^{'}))}^{'} + c (t) Φ (y) = 0, Φ (s) : = {| s |}^{p - 2} s . (*)$ 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.