zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Oscillation of second-order damped dynamic equations on time scales. (English) Zbl 1128.34022

The authors study the oscillation of the solutions of the nonlinear second order dynamic equation with damping

(a(t)x Δ (t)) Δ +p(t)x Δ σ (t)+q(t)(fx σ )=0

on a time scale 𝕋, that is, on a nonempty closed subset of the real numbers. (For the definition of (delta) derivative and other related notions on dynamic equations, the reader is referred to [M. Bohner and A. Peterson, Dynamic equations on time scales: An introduction with applications. Basel: Birkhäuser (2001; Zbl 0978.39001)]). By imposing appropriate conditions (too involved to be described here) to the maps a,p,q and f, the authors establish a series of results ensuring the oscillatory character of the above mentioned dynamic equation. It is worth mentioning that by using this general approach of time scales, the authors unify the study of differential and difference equations (when 𝕋= and 𝕋=, respectively), and extend and improve some known results existing already in the literature. Moreover, they obtain new results for the time scales 𝕋=h, h>0,𝕋=q , q>1, among others.

34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
39A12Discrete version of topics in analysis