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 nonoscillation of mixed advanced-delay differential equations with positive and negative coefficients. (English) Zbl 1197.34118

Summary: For the mixed (advanced-delay) differential equation with variable delays and coefficients

x ˙(t)±a(t)x(g(t))b(t)x(h(t))=0,tt 0

where

a(t)0,b(t)0,g(t)t,h(t)t

explicit nonoscillation conditions are obtained.

MSC:
34K11Oscillation theory of functional-differential equations
References:
[1]Frish, R.; Holme, H.: The characteristic solutions of mixed difference and differential equation occurring in economic dynamics, Econometrica 3, No. 2, 225-239 (1935) · Zbl 61.1326.05 · doi:10.2307/1907258
[2]Gandolfo, G.: Economic dynamics, (1996)
[3]James, R. W.; Belz, M. H.: The significance of the characteristic solutions of mixed difference and differential equations, Econometrica 6, No. 4, 326-343 (1938) · Zbl 64.0448.02
[4]Asada, T.; Yoshida, H.: Stability, instability and complex behavior in macrodynamic models with policy lag, Discrete dyn. Nat. and soc. 5, 281-295 (2000) · Zbl 0980.34070 · doi:10.1155/S1026022600000583
[5]Dubois, D. M.: Extension of the kaldor–kalecki model of business cycle with a computational anticipated capital stock, J. organ. Trans. soc. Change 1, No. 1, 63-80 (2004)
[6]Kaddar, A.; Alaoui, H. T.: Fluctuations in a mixed IS-LM business cycle models, Electron. J. Differential equations 2008, No. 34, 1-9 (2008)
[7]Ladde, G. S.; Lakshmikantham, V.; Zhang, B. G.: Oscillation theory of differential equations with deviating arguments, (1987)
[8]Györi, I.; Ladas, G.: Oscillation theory of delay differential equations, (1991) · Zbl 0780.34048
[9]Ladde, G. S.; Lakshmikantham, V.; Zhang, B. G.: Oscillation theory of differential equations with deviating arguments, (1987)
[10]Gopalsamy, K.: Stability and oscillation in delay differential equations of popular dynamics, (1992) · Zbl 0752.34039
[11]Agarwal, R. P.; Bohner, M.; Li, W. -T.: Nonoscillation and oscillation: theory for functional differential equations, Monographs and textbooks in pure and applied mathematics 267 (2004) · Zbl 1068.34002
[12]Kordonis, I. -G.E.; Philos, Ch.G.: Oscillation and nonoscillation in delay or advanced differential equations and in integrodifferential equations, Georgian math. J. 6, 263-284 (1999) · Zbl 0930.34050 · doi:10.1023/A:1022135230680 · doi:emis:journals/GMJ/vol6/contents.htm
[13]Meng, Q.; Yan, J.: Nonautonomous differential equations of alternately retarded and advanced type, Int. J. Math. math. Sci. 26, No. 10, 597-603 (2001) · Zbl 1004.34060 · doi:10.1155/S0161171201005592
[14]Li, X.; Zhu, D.; Wang, H.: Oscillation for advanced differential equations with oscillating coefficients, Int. J. Math. math. Sci. 28, No. 33, 2109-2118 (2003) · Zbl 1031.34066 · doi:10.1155/S0161171203209030
[15]Markova, N. T.; Simeonov, P. S.: Oscillation criteria for first order nonlinear differential equations with advanced arguments, Commun. appl. Anal. 10, No. 2–3, 209-221 (2006) · Zbl 1123.34052
[16]Agarwal, R. P.; Grace, S. R.; O’regan, D.: On the oscillation of certain advanced functional differential equations using comparison methods, Fasc. math., No. 35, 5-22 (2005) · Zbl 1099.34059
[17]Kiguradze, I. T.; Partsvaniya, N. L.; Stavroulakis, I. P.: On the oscillatory properties of higher-order advance functional-differential equations, Differ. equ. 38, No. 8, 1095-1107 (2002) · Zbl 1042.34095 · doi:10.1023/A:1021612003320
[18]Li, X.; Zhu, D.: Oscillation and nonoscillation of advanced differential equations with variable coefficients, J. math. Anal. appl. 269, No. 2, 462-488 (2002) · Zbl 1013.34067 · doi:10.1016/S0022-247X(02)00029-X
[19]Litsyn, E.; Stavroulakis, I. P.: On the oscillation of solutions of higher order Emden–Fowler state dependent advanced differential equations, Nonlinear anal. 47, No. 6, 3877-3883 (2001) · Zbl 1042.34563 · doi:10.1016/S0362-546X(01)00507-7
[20]Ladas, G.; Stavroulakis, I. P.: Oscillations of differential equations of mixed type, J. math. Phys. sci. 18, No. 3, 245-262 (1984) · Zbl 0654.34058
[21]Ladas, G.; Schults, S. W.: On oscillations of neutral equations with mixed arguments, Hiroshima math. J. 19, No. 2, 409-429 (1989) · Zbl 0697.34060
[22]Rustichini, A.: Functional-differential equations of mixed type: the linear autonomous case, J. dynam. Differential equations 1, No. 2, 121-143 (1989) · Zbl 0684.34065 · doi:10.1007/BF01047828
[23]Stavroulakis, I. P.: Oscillations of mixed neutral equations, Hiroshima math. J. 19, No. 3, 441-456 (1989) · Zbl 0712.34078
[24]Grammatikopoulos, M. K.; Stavroulakis, I. P.: Oscillations of neutral differential equations, Rad. mat. 7, No. 1, 47-71 (1991) · Zbl 0742.34062
[25]Kusano, T.: On even-order functional-differential equations with advanced and retarded arguments, J. differential equations 45, No. 1, 75-84 (1982) · Zbl 0512.34059 · doi:10.1016/0022-0396(82)90055-9
[26]Ivanov, A. F.; Kitamura, Y.; Kusano, T.; Shevelo, V. N.: Oscillatory solutions of functional-differential equations generated by deviation of arguments of mixed type, Hiroshima math. J. 12, No. 3, 645-655 (1982) · Zbl 0511.34052
[27]Džurina, J.: Oscillation of second-order differential equations with mixed argument, J. math. Anal. appl. 190, No. 3, 821-828 (1995) · Zbl 0824.34073 · doi:10.1006/jmaa.1995.1114
[28]Yan, J. R.: Comparison theorems for differential equations of mixed type, Ann. differential equations 7, No. 3, 316-322 (1991) · Zbl 0742.34066
[29]Gopalsamy, K.: Nonoscillatory differential equations with retarded and advanced arguments, Quart. appl. Math. 43, No. 2, 211-214 (1985) · Zbl 0589.34053
[30]Nadareishvili, V. A.: Oscillation and nonoscillation of first order linear differential equations with deviating arguments, Differ. equ. 25, No. 4, 412-417 (1989) · Zbl 0694.34055
[31]Berezansky, L.; Domshlak, Y.: Differential equations to several delays: Sturmian comparison method in oscillation theory, II, Electron. J. Differential equations 2002, No. 31, 1-18 (2002) · Zbl 1016.34066 · doi:emis:journals/EJDE/Volumes/2002/31/abstr.html
[32]Berezansky, L.; Braverman, E.: On non-oscillation of a scalar delay differential equation, Dynam. systems appl. 6, 567-581 (1997) · Zbl 0890.34059
[33]Rath, R.; Mishra, P. P.; Padhy, L. N.: On oscillation and asymptotic behaviour of a neutral differential equation of first order with positive and negative coefficients, Electron. J. Differential equations 2007, No. 1, 1-7 (2007) · Zbl 1118.34054 · doi:emis:journals/EJDE/Volumes/2007/01/abstr.html
[34]Dix, J. G.; Misra, N.; Padhy, L.; Rath, R.: Oscillatory and asymptotic behaviour of a neutral differential equation with oscillating coefficients, Electron. J. Qual. theory differ. Equ., No. 19, 1-10 (2008) · Zbl 1183.34107 · doi:emis:journals/EJQTDE/2008/200819.html
[35]Karpuz, B.; Manojlović, J. V.; Öcalan, Ö.; Shoukaku, Y.: Oscillation criteria for a class of second-order neutral delay differential equations, Appl. math. Comput. 210, No. 2, 303-312 (2009) · Zbl 1188.34087 · doi:10.1016/j.amc.2008.12.075
[36]Berezansky, L.; Domshlak, Yu.; Braverman, E.: On oscillation properties of delay differential equations with positive and negative coefficients, J. math. Anal. appl. 274, No. 1, 81-101 (2002) · Zbl 1056.34063 · doi:10.1016/S0022-247X(02)00246-9