JournalszaaVol. 31, No. 2pp. 203–216

On Monotonicity of Nonoscillation Properties of Dynamic Equations in Time Scales

  • Elena Braverman

    Technion - Israel Institute of Technology, Haifa, Israel
  • Bașak Karpuz

    Afyon Kocatepe University, Afyonkarahisar, Turkey
On Monotonicity of Nonoscillation Properties of Dynamic Equations in Time Scales cover
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Abstract

For equations on time scales, we consider the following problem: when will nonoscillation on time scale T\mathbb T imply nonoscillation of the same equation on any time scale T~\tilde {\mathbb T} including T\mathbb T as a subset? The main result of the paper is the following. If nonnegative coefficients Ak(t)A_k(t) are nonincreasing and αk(t)t\alpha_k(t) ≤ t are nondecreasing in tRt \in \mathbb R, then nonoscillation of the equation

x^{\Delta} (t) +\sum^m_{k=1} A_k(t)x(\alpha_k(t)) = 0 \ \ \ \rm{for} \ t \in [t_0,\infty)_{\mathbb T}

yields nonoscillation of the same equation on any time scale T~T\tilde {\mathbb T} \supset T.

Cite this article

Elena Braverman, Bașak Karpuz, On Monotonicity of Nonoscillation Properties of Dynamic Equations in Time Scales. Z. Anal. Anwend. 31 (2012), no. 2, pp. 203–216

DOI 10.4171/ZAA/1455