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

Došlý, Ondřej

Czechoslovak Mathematical Journal, Tome 50 (2000) no. 3, pp. 657-671

Abstract (VO)

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.

Détail

Classification : 34C10
Keywords: half-linear equation; Riccati technique; variational principle; reciprocity principle; principal solution; oscillation and nonoscillation criteria

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