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 results for second-order linear equations on a time scale. (English) Zbl 1021.34012
The author considers the second-order scalar dynamic equation $$(r(t)x^\Delta(t))^\Delta+q(t)x^\sigma(t)=0\tag*$$ on a time scale ${\Bbb T}$, where $\sup{\Bbb T}=\infty$, $r:{\Bbb T}\rightarrow{\Bbb R}^+$ is assumed to be rd-continuously differentiable, $q:{\Bbb T}\rightarrow{\Bbb R}$ is rd-continuous and the graininess $\mu$ is not identically zero on $[\tau,\infty)\cap{\Bbb T}$, for large $\tau\in{\Bbb T}$. Using averaging techniques, criteria for the oscillatory behavior of $(\ast)$ are deduced, which extend earlier results by the author for difference equations in [J. Math. Anal. Appl., 142, No. 2, 468--487 (1989, Zbl 0686.39001)]. In particular, these criteria indicate how oscillation depends on the graininess of the time scale. Finally, two examples illustrate the obtained results.

34B10Nonlocal and multipoint boundary value problems for ODE
39A13Difference equations, scaling ($q$-differences)
Full Text: DOI