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Summation comparison theorems for half-linear second order difference equations on finite interval

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  • Robert Mařík

    (Ústav matematiky, Mendelova univerzita v Brně, Zemědělská 1, 613 00 Brno, Česká republika)

Abstract

In the paper, new comparison theorems for the half-linear difference equationΔ(RkΦ(Δzk)) + CkΦ(zk+1) = 0, Φ(u) = |u|p-2 u, p > 1,are derived. We show that if a solution of this equation has a generalized zero on the discrete interval [a, b], then the same holds for a solution of its majorant. The main tool used in the paper is the variational technique which relates nonexistence of a solution with a generalized zero with nonegativity of the p-degree functional defined on the suitable class of admissible functions.

Suggested Citation

  • Robert Mařík, 2011. "Summation comparison theorems for half-linear second order difference equations on finite interval," Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, Mendel University Press, vol. 59(7), pages 245-248.
    • Handle: RePEc:mup:actaun:actaun_2011059070245
    DOI: 10.11118/actaun201159070245
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