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Necessary and Sufficient Conditions for Positive Solutions of Second-Order Nonlinear Dynamic Equations on Time Scales

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  • Zhi-Qiang Zhu

Abstract

This paper is concerned with the existence of nonoscillatory solutions for the nonlinear dynamic equation ( ð ‘ ( ð ‘¡ ) ( 𠜓 ∘ ð ‘¥ ) ( ð ‘¥ 𠜎 ) Δ ) Δ + ð ‘ž ( ð ‘¡ ) ð ‘“ ∘ ð ‘¥ 𠜎 = 0 on time scales. By making use of the generalized Riccati transformation technique, we establish some necessary and sufficient criteria to guarantee the existence. The last examples show that our results can be applied on the differential equations, the difference equations, and the ð ‘ž -difference equations.

Suggested Citation

  • Zhi-Qiang Zhu, 2011. "Necessary and Sufficient Conditions for Positive Solutions of Second-Order Nonlinear Dynamic Equations on Time Scales," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2011, pages 1-11, June.
    • Handle: RePEc:hin:jijmms:769893
    DOI: 10.1155/2011/769893
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