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 nonlinear neutral differential equations. (English) Zbl 1026.34081
Summary: Consider the second-order nonlinear neutral delay differential equation $$\Bigl[r(t) \biggl(\bigl(x(t)+ p(t)x(t-\tau)\bigr)' \biggr)^\alpha \Bigr]'+f \bigl(t,x(t- \sigma)\bigr) =0,\tag E$$ where $\tau$ and $\sigma$ are nonnegative constants, and $\alpha$ is a quotient of positive odd integers. Some new oscillatory criteria for (E) are established. Several examples which dwell upon the importance of our results are illustrated, too.

34K11Oscillation theory of functional-differential equations
34K40Neutral functional-differential equations
Full Text: DOI
[1] Hartman, P.: Ordinary differential equations. (1982) · Zbl 0476.34002
[2] Grammatikopoules, M. K.; Ladas, G.; Meimaridou, A.: Oscillation of second order neutral delay differential equations. Rat. math. 1, 267-274 (1985) · Zbl 0581.34051
[3] Ruan, S.: Oscillation of second order neutral differential equations. Canad. math. Bull. 36, 485-496 (1993) · Zbl 0798.34079
[4] Philos, C. G.: Oscillation theorems for linear differential equation of second order. Arch. math. 53, 483-492 (1989) · Zbl 0661.34030
[5] Li, H. J.; Liu, W. L.: Oscillation criteria for second order neutral differential equations. Canad. J. Math. 48, 871-886 (1996) · Zbl 0859.34055
[6] Lou, J. W.: Oscillation of second order nonlinear neutral differential equations. J. shaoying teachers college 20, No. 5, 17-25 (1998)
[7] Jiang, J. C.: Oscillation and nonoscillation theorems for second order nonlinear differential equations. Tamkang. J. Math. 32, No. 2, 95-102 (2001) · Zbl 0999.34038
[8] Wang, J. F.: On second order quasilinear oscillations. Funkcial. ekvac. 41, 25-54 (1998) · Zbl 1140.34356
[9] Del Pino, M.; Manasevich, R.: Some nonlinear Sturmian comparison theory for (|u’|p-2u’)’+$c(t)$|u|p-$2{\cdot}$u=0. Lecture notes in pure and applied mathematics 118, 183-190 (1989)