On certain comparison theorems for half‐linear dynamic equations on time scales

Pavel Řehák

Abstract and Applied Analysis, 2004, vol. 2004, issue 7, 551-565

Abstract: We obtain comparison theorems for the second‐order half‐linear dynamic equation [r(t)Φ(yΔ)]Δ+p(t)Φ(yσ)=0, where Φ(x) = |x|α−1sgn x with α > 1. In particular, it is shown that the nonoscillation of the previous dynamic equation is preserved if we multiply the coefficient p(t) by a suitable function q(t) and lower the exponent α in the nonlinearity Φ, under certain assumptions. Moreover, we give a generalization of Hille‐Wintner comparison theorem. In addition to the aspect of unification and extension, our theorems provide some new results even in the continuous and the discrete case.

Date: 2004
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https://doi.org/10.1155/S1085337504306251

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2004:y:2004:i:7:p:551-565

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