𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Oscillation of second-order half-linear delay dynamic equations with damping on time scales

✍ Scribed by Quanxin Zhang

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
258 KB
Volume
235
Category
Article
ISSN
0377-0427

No coin nor oath required. For personal study only.

✦ Synopsis

By using the generalized Riccati transformation and the inequality technique, we establish a few new oscillation criterions for certain second-order half-linear delay dynamic equations with damping on a time scale. Our results extend and improve some known results, but also unify the oscillation of the second-order half-linear delay differential equation with damping and the second-order half-linear delay difference equation with damping.

πŸ“œ SIMILAR VOLUMES

New comparison and oscillation theorems
New comparison and oscillation theorems for second-order half-linear dynamic equations on time scales
✍ Baoguo Jia; Lynn Erbe; Allan Peterson πŸ“‚ Article πŸ“… 2008 πŸ› Elsevier Science 🌐 English βš– 338 KB

a b s t r a c t Let T be a time scale (i.e., a closed nonempty subset of R) with sup T = +∞. Consider the second-order half-linear dynamic equation where r(t) > 0, p(t) are continuous, In particular, no explicit sign assumptions are made with respect to the coefficient p(t). We give conditions und

Nonlinear oscillation of second-order dy
Nonlinear oscillation of second-order dynamic equations on time scales
✍ Douglas R. Anderson; A. Zafer πŸ“‚ Article πŸ“… 2009 πŸ› Elsevier Science 🌐 English βš– 471 KB

Interval oscillation criteria are established for a second-order nonlinear dynamic equation on time scales by utilizing a generalized Riccati technique and the Young inequality. The theory can be applied to second-order dynamic equations regardless of the choice of delta or nabla derivatives.

Oscillation of third order nonlinear del
Oscillation of third order nonlinear delay dynamic equations on time scales
✍ Taher S. Hassan πŸ“‚ Article πŸ“… 2009 πŸ› Elsevier Science 🌐 English βš– 833 KB

It is the purpose of this paper to give oscillation criteria for the third order nonlinear delay dynamic equation on a time scale T, where Ξ³ β‰₯ 1 is the quotient of odd positive integers, a and r are positive rd-continuous functions on T, and the so-called delay function Ο„ : T β†’ T satisfies Ο„ (t) ≀