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)
Existence of nonoscillatory solutions of higher-order neutral differential equations with positive and negative coefficients. (English) Zbl 1025.34065
The authors consider the following higher-order neutral functional-differential equations with positive and negative coefficients: $$ \frac{d^n}{dt^n}[x(t)+cx(t-\tau)]+(-1)^{n+1}[P(t)x(t-\sigma)-Q(t)x(t-\delta)]=0,\quad t\geq t_0, $$ where $n\geq 1$ is an integer, $c\in \bbfR, \tau, \sigma, \delta \in\bbfR^+$, and $P, Q\in C([t_0, \infty), \bbfR^+), \bbfR^+=[0, \infty)$. They obtain global results (with respect to $c$) which are some sufficient conditions for the existence of nonoscillatory solutions.

MSC:
34K11Oscillation theory of functional-differential equations
34K40Neutral functional-differential equations
WorldCat.org
Full Text: DOI
References:
[1] Agarwal, R. P.; Grace, S. R.; O’regan, D.: Oscillation theory for difference and functional differential equations. (2000)
[2] Erbe, L. H.; Kong, Q. K.; Zhang, B. G.: Oscillation theory for functional differential equations. (1995) · Zbl 0821.34067
[3] Gyori, I.; Ladas, G.: Oscillation theory for delay differential equations with applications. (1991)
[4] Kulenović, M. R. S.; Hadz\hat{}iomerspahić, S.: Existence of nonoscillatory solution of second order linear neutral delay equation. J. math. Anal. appl. 228, 436-448 (1998) · Zbl 0919.34067
[5] Tanaka, S.: Existence of positive solutions of higher order nonlinear neutral differential equations. Rocky mountain J. Math. 30, 1139-1149 (2000) · Zbl 0984.34068
[6] Tanaka, S.: Oscillatory and nonoscillatory solutions of neutral differential equations. Ann. polonici math. 2, 169-184 (2000) · Zbl 0971.34056
[7] Zhang, B. G.; Yang, B.: New approach of studying the oscillation of neutral differential equations. Funkcial. ekvac. 41, 79-89 (1998) · Zbl 1140.34439
[8] Zhang, B. G.; Yu, J. S.: On the existence of asymptotically decaying positive solutions of second order neutral differential equations. J. math. Anal. appl. 166, 1-11 (1992) · Zbl 0754.34075
[9] Zhang, B. G.; Yu, J. S.; Wang, Z. C.: Oscillations of higher order neutral differential equations. Rocky mountain J. Math. 25, 557-568 (1995) · Zbl 0832.34075
[10] Graef, J. R.; Yang, B.; Zhang, B. G.: Existence of nonoscillatory and oscillatory solutions of neutral differential equations with positive and negative coefficients. Math. boh. 124, 87-102 (1999) · Zbl 0937.34066
[11] Zhang, B. G.: On the positive solutions of a kind of neutral equations. Acta math. Appl. sinica 19, No. 2, 222-230 (1996) · Zbl 0859.34059
[12] Agarwal, R. P.; Grace, S. R.: Oscillation theorems for certain of neutral functional differential equations. Computers math. Applic. 38, No. 11/12, 1-11 (1999) · Zbl 0981.34059
[13] Zhou, Y.: Oscillation of neutral functional differential equations. Acta math. Hungar. 86, 205-212 (2000) · Zbl 0955.34050