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)
Asymptotic properties of solutions to $n$-dimensional neutral differential systems. (English) Zbl 1176.34090
Summary: We consider neutral functional differential systems $$\aligned [y_1(t)-a(t)y_1(g(t))]' & =p_1(t)y_2(t),\\ y'_i(t) & = p_i(t)y_{i+1}(t),\quad i=2,3,\dots,n-1,\\ y_n'(t)& = \sigma p_n(t)f(y_1(h(t))),\quad t\ge t_0,\endaligned$$ where $n\ge 3$, $\sigma=1$ or $\sigma=-1$. We find sufficient conditions for solutions either to be oscillatory or to decay to zero. One example is included.

MSC:
34K25Asymptotic theory of functional-differential equations
34K11Oscillation theory of functional-differential equations
34K40Neutral functional-differential equations
WorldCat.org
Full Text: DOI
References:
[1] Marušiak, P.: On unbonded nonoscillatory solutions of systems of neutral differential equations. Czechoslovak math. J. 42, No. 117, 117-128 (1992) · Zbl 0758.34055
[2] Erbe, L. H.; Kong, -Q.; Zhang, -B.G.: Oscillation theory for functional differential equations. (1995)
[3] Grace, S. R.; Lalli, B. S.: Oscillation theorems for certain neutral differential equations. Czechoslovak math. J. 38, No. 113, 745-753 (1988) · Zbl 0705.34072
[4] Marušiak, P.: Asymptotic properties of nonoscillatory solutions of neutral delay differential equations of n-th order. Czechoslovak math. J. 47, No. 122, 327-336 (1997) · Zbl 0937.34065
[5] Ru\dot{}žičková, M.; Špániková, E.: Oscillation theorems for neutral differential equations with the quasi-derivatives. Arch. math. 30, No. 4, 293-300 (1994)
[6] Ru\dot{}žičková, M.; Špániková, E.: Oscillation of functional differential equations of neutral type with the quasi-derivatives. Fasc. math. 26, 139-146 (1996) · Zbl 0862.34051
[7] Bartušek, M.: Oscillatory criteria for nonlinear nth-order differential equations with quasiderivatives. Georgia math. J. 3, No. 4, 301-314 (1996) · Zbl 0857.34038
[8] Ivanov, A. F.; Marušiak, P.: Oscillatory properties of systems of neutral differential equations. Hiroshima math. J. 24, 423-434 (1994) · Zbl 0811.34054
[9] Marušiak, P.: Oscillatory properties of functional differential systems of neutral type. Czechoslovak math. J. 43, No. 118, 649-662 (1993) · Zbl 0801.34071
[10] Mihalíková, B.: Asymptotic behaviour of solutions of two-dimensional neutral differential systems. Czechoslovak math. J. 53, No. 128, 735-741 (2003) · Zbl 1080.34555
[11] B. Mihalíková, J. Džurina, On the oscillation of bounded solutions of systems of neutral differential equations, in: Proceedings of the International Scientific Conference of Mathematics, University of Žilina, 1998, pp. 189--194
[12] Mihály, T.: On the oscillatory and asymptotic properties of solutions of systems of neutral differential equations. Nonlinear anal. 66, 2053-2063 (2007) · Zbl 1121.34083
[13] Špániková, E.; Šamajová, H.: Asymptotic behaviour of non-oscillatory solutions of neutral differential systems. Studies of the university of žilina, math. Series 17, 147-152 (2003)
[14] Špániková, E.: Oscillation of differential systems of neutral type. Czechoslovak math. J. 55, No. 130, 263-271 (2005)
[15] Staněk, S.: Oscillation behaviour of solutions of neutral delay differential equations. Časopis pro pěstování matematiky 115, No. 1, 92-99 (1990)
[16] Olach, R.: Oscillation of differential equation of neutral type. Hiroshima math. J. 25, 1-10 (1995)
[17] Jaroš, J.; Kusano, T.: On a class of first order nonlinear functional differential equations of neutral type. Czechoslovak math. J. 40, No. 115, 475-490 (1990) · Zbl 0728.34083