zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
On the oscillation of certain functional differential equations via comparison methods. (English) Zbl 1057.34072
Several oscillation criteria for functional-differential equations of the form $$ \frac{d}{dt}\left( \left[ \frac{1}{a_{n-1}(t)}\frac{d}{dt} \frac{1}{a_{n-2}(t)}\frac{d}{dt}\dots\frac{1}{a_{1}(t)}\frac{d}{dt}x(t) \right] ^{a}\right) \pm q(t)f(x[g(t)])=0 $$ are established.

MSC:
34K11Oscillation theory of functional-differential equations
WorldCat.org
Full Text: DOI
References:
[1] Agarwal, R. P.; Grace, S. R.: Oscillation of certain functional differential equations. Comput. math. Appl. 38, 143-153 (1999) · Zbl 0935.34059
[2] Agarwal, R. P.; Grace, S. R.: On the oscillation of higher order differential equations with deviating arguments. Comput. math. Appl. 38, 185-199 (1999) · Zbl 0935.34058
[3] Agarwal, R. P.; Grace, S. R.; O’regan, D.: Oscillation theory for difference and functional differential equations. (2000)
[4] Agarwal, R. P.; Grace, S. R.; O’regan, D.: Oscillation theory for second order linear, half-linear, superlinear and sublinear dynamic equations. (2002) · Zbl 1073.34002
[5] Agarwal, R. P.; Grace, S. R.; O’regan, D.: Oscillation theory for second order dynamic equations. (2003) · Zbl 1043.34032
[6] Agarwal, R. P.; Grace, S. R.; O’regan, D.: Oscillation criteria for certain nth order differential equations with deviating arguments. J. math. Anal. appl. 262, 601-622 (2001) · Zbl 0997.34060
[7] R.P. Agarwal, S.R. Grace, D. O’Regan, On the oscillation of certain higher order functional differential equations, Math. Comput. Modelling, submitted for publication
[8] Kitamura, Y.: Oscillation of functional differential equations with general deviating arguments. Hiroshima math. J. 15, 445-491 (1985) · Zbl 0599.34091
[9] Kusano, T.; Lalli, B. S.: On oscillation of half-linear functional differential equations with deviating arguments. Hiroshima math. J. 24, 549-563 (1994) · Zbl 0836.34081
[10] Kusano, T.; Naito, M.: Comparison theorems for functional differential equations with deviating arguments. J. math. Soc. Japan 33, 509-532 (1981) · Zbl 0494.34049
[11] Philos, Ch.G.: On the existence of nonoscillatory solutions tending to zero at $\infty $for differential equations with positive delays. Arch. math. 36, 168-178 (1981) · Zbl 0463.34050