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

Pavel Řehák

Abstract and Applied Analysis, 2004, vol. 2004, 1-15

Abstract:

We obtain comparison theorems for the second-order half-linear dynamic equation [ r ( t ) Φ ( y Δ ) ] Δ + p ( t ) Φ ( y σ ) = 0 , where Φ ( x ) = | x | α − 1 sgn 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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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:987283

DOI: 10.1155/S1085337504306251

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