Hille-kneser-type Criteria for Second-order Dynamic Equations on Time Scales

  title={Hille-kneser-type Criteria for Second-order Dynamic Equations on Time Scales},
  author={Lynn Erbe and Allan Peterson and Samir H. Saker},
We consider the pair of second-order dynamic equations, (r(t)(xΔ)γ)Δ + p(t)xγ(t) = 0 and (r(t)(xΔ)γ)Δ + p(t)xγσ(t) = 0, on a time scale T, where γ > 0 is a quotient of odd positive integers. We establish some necessary and sufficient conditions for nonoscillation of Hille-Kneser type. Our results in the special case when T = R involve the wellknown Hille-Kneser-type criteria of second-order linear differential equations established by Hille. For the case of the second-order half-linear… CONTINUE READING

From This Paper

Topics from this paper.
10 Citations
32 References
Similar Papers


Publications citing this paper.
Showing 1-10 of 10 extracted citations


Publications referenced by this paper.
Showing 1-10 of 32 references

Non-oscillation theorems

  • E. Hille
  • Transactions of the American Mathematical Society…
  • 1948
Highly Influential
16 Excerpts

Half-Linear Differential Equations

  • O. Došlý, P. Řehák
  • North-Holland Mathematics Studies, vol. 202…
  • 2005
Highly Influential
9 Excerpts

Sturmian comparison theorem for half-linear second-order differential equations

  • H. J. Li, C. C. Yeh
  • Proceedings of the Royal Society of Edinburgh…
  • 1995
Highly Influential
4 Excerpts

Nonoscillation theorems for a class of quasilinear differential equations of second order

  • T. Kusano, N. Yoshida
  • Journal of Mathematical Analysis and Applications…
  • 1995
Highly Influential
2 Excerpts

Similar Papers

Loading similar papers…