Oscillation Theorems for Second-Order Half-Linear Advanced Dynamic Equations on Time Scales

Shuhong Tang, Tongxing Li and Ethiraju Thandapani

International Journal of Differential Equations, 2011, vol. 2011, 1-16

Abstract:

This paper is concerned with the oscillatory behavior of the second-order half-linear advanced dynamic equation ( ð ‘Ÿ ( ð ‘¡ ) ( ð ‘¥ Δ ( ð ‘¡ ) ) ð ›¾ ) Δ + ð ‘ ( ð ‘¡ ) ð ‘¥ ð ›¾ ( ð ‘” ( ð ‘¡ ) ) = 0 on an arbitrary time scale ð •‹ with sup ð •‹ = ∞ , where ð ‘” ( ð ‘¡ ) ≥ ð ‘¡ and ∫ ∞ ð ‘¡ ð ‘œ ( Δ ð ‘ / ( ð ‘Ÿ 1 / ð ›¾ ( ð ‘ ) ) ) < ∞ . Some sufficient conditions for oscillation of the studied equation are established. Our results not only improve and complement those results in the literature but also unify the oscillation of the second-order half-linear advanced differential equation and the second-order half-linear advanced difference equation. Three examples are included to illustrate the main results.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijde:840569

DOI: 10.1155/2011/840569

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