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Title: Positive solutions of third order damped nonlinear differential equations (English)
Author: Bartušek, Miroslav
Author: Cecchi, Mariella
Author: Došlá, Zuzana
Author: Marini, Mauro
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 136
Issue: 2
Year: 2011
Pages: 205-213
Summary lang: English
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Category: math
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Summary: We study solutions tending to nonzero constants for the third order differential equation with the damping term \[ (a_{1}(t)(a_{2}(t)x'(t))')'+q(t)x'(t)+r(t)f(x(\varphi (t)))=0 \] in the case when the corresponding second order differential equation is oscillatory. (English)
Keyword: third order differential equation
Keyword: damping term
Keyword: second order oscillatory equation
Keyword: positive solution
Keyword: asymptotic properties
MSC: 34C10
MSC: 34D05
MSC: 34K11
MSC: 34K25
idZBL: Zbl 1224.34152
idMR: MR2856137
DOI: 10.21136/MB.2011.141583
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Date available: 2011-06-07T11:31:58Z
Last updated: 2020-07-29
Stable URL: http://hdl.handle.net/10338.dmlcz/141583
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Reference: [1] Agarwal, R., Aktas, M. F., Tiryaki, A.: On oscillation criteria for third order nonlinear delay differential equations.Arch. Math. (Brno) 45 (2009), 1-18. Zbl 1212.34189, MR 2591657
Reference: [2] Baculikova, B., Elabbasy, E. M., Saker, S. H., Dzurina, J.: Oscillation criteria for third-order nonlinear differential equations.Math. Slovaca 58 (2008), 201-202. Zbl 1174.34052, MR 2391214, 10.2478/s12175-008-0068-1
Reference: [3] Bartušek, M., Cecchi, M., Došlá, Z., Marini, M.: On nonoscillatory solutions of third order nonlinear differential equations.Dynam. Systems Appl. 9 (2000), 483-500. MR 1843694
Reference: [4] Bartušek, M., Cecchi, M., Došlá, Z., Marini, M.: Oscillation for third order nonlinear differential equations with deviating argument.Abstr. Appl. Anal. 2010, Article ID 278962, 19 p. (2010). Zbl 1192.34073, MR 2587610
Reference: [5] Bartušek, M., Cecchi, M., Marini, M.: On Kneser solutions of nonlinear third order differential equations.J. Math. Anal. Appl. 261 (2001), 72-84. Zbl 0995.34025, MR 1850957, 10.1006/jmaa.2000.7473
Reference: [6] Cecchi, M., Došlá, Z., Marini, M.: On third order differential equations with property A and B.J. Math. Anal. Appl. 231 (1999), 509-525. MR 1669163, 10.1006/jmaa.1998.6247
Reference: [7] Cecchi, M., Došlá, Z., Marini, M.: On nonlinear oscillations for equations associated to disconjugate operators.Nonlinear Anal., Theory Methods Appl. 30 (1997), 1583-1594. MR 1490081, 10.1016/S0362-546X(97)00028-X
Reference: [8] Coles, W. J.: Boundedness of solutions of two-dimensional first order differential systems.Boll. Un. Mat. Ital. 4 (1971), 225-231. Zbl 0229.34027, MR 0293162
Reference: [9] Jaroš, J., Kusano, T., Marić, V.: Existence of regularly and rapidly varying solutions for a class of third order nonlinear ordinary differential equations.Publ. Inst. Math. Beograd 79 (2006), 51-64. MR 2275338, 10.2298/PIM0693051J
Reference: [10] Kiguradze, I.: An oscillation criterion for a class of ordinary differential equations.Diff. Urav. 28 (1992), 201-214. Zbl 0768.34018, MR 1184921
Reference: [11] Marini, M.: Criteri di limitatezza per le soluzioni dell'equazione lineare del secondo ordine.Boll. Un. Mat. Ital. 11 (1975), 154-165. Zbl 0332.34027, MR 0372326
Reference: [12] Mojsej, I.: Asymptotic properties of solutions of third-order nonlinear differential equations with deviating argument.Nonlinear Analysis 68 (2008), 3581-3591. Zbl 1151.34053, MR 2401369, 10.1016/j.na.2007.04.001
Reference: [13] Mojsej, I., Ohriska, J.: Comparison theorems for noncanonical third order nonlinear differential equations.Central Eur. J. Math. 5 (2007), 154-16. Zbl 1128.34021, MR 2287717, 10.2478/s11533-006-0044-3
Reference: [14] Saker, S. H.: Oscillation criteria of Hille and Nehari types for third order delay differential equations.Commun. Appl. Anal. 11 (2007), 451-468. Zbl 1139.34049, MR 2368196
Reference: [15] Tiryaki, A., Aktas, M. F.: Oscillation criteria of a certain class of third order nonlinear delay differential equations with damping.J. Math. Anal. Appl. 325 (2007), 54-68. Zbl 1110.34048, MR 2273028, 10.1016/j.jmaa.2006.01.001
Reference: [16] Tunc, C.: On the non-oscillation of solutions of some nonlinear differential equations of third order.Nonlinear Dyn. Syst. Theory 7 (2007), 419-430. Zbl 1140.34415, MR 2367678
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