Positive solutions of third order damped nonlinear differential equations

Miroslav Bartušek; Mariella Cecchi; Zuzana Došlá; Mauro Marini

Mathematica Bohemica (2011)

  • Volume: 136, Issue: 2, page 205-213
  • ISSN: 0862-7959

Abstract

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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 ( ϕ ( t ) ) ) = 0 in the case when the corresponding second order differential equation is oscillatory.

How to cite

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Bartušek, Miroslav, et al. "Positive solutions of third order damped nonlinear differential equations." Mathematica Bohemica 136.2 (2011): 205-213. <http://eudml.org/doc/196383>.

@article{Bartušek2011,
abstract = {We study solutions tending to nonzero constants for the third order differential equation with the damping term \[ (a\_\{1\}(t)(a\_\{2\}(t)x^\{\prime \}(t))^\{\prime \})^\{\prime \}+q(t)x^\{\prime \}(t)+r(t)f(x(\varphi (t)))=0 \] in the case when the corresponding second order differential equation is oscillatory.},
author = {Bartušek, Miroslav, Cecchi, Mariella, Došlá, Zuzana, Marini, Mauro},
journal = {Mathematica Bohemica},
keywords = {third order differential equation; damping term; second order oscillatory equation; positive solution; asymptotic properties; third order differential equation; damping term; second order oscillatory equation; positive solution; asymptotic property},
language = {eng},
number = {2},
pages = {205-213},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Positive solutions of third order damped nonlinear differential equations},
url = {http://eudml.org/doc/196383},
volume = {136},
year = {2011},
}

TY - JOUR
AU - Bartušek, Miroslav
AU - Cecchi, Mariella
AU - Došlá, Zuzana
AU - Marini, Mauro
TI - Positive solutions of third order damped nonlinear differential equations
JO - Mathematica Bohemica
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 136
IS - 2
SP - 205
EP - 213
AB - We study solutions tending to nonzero constants for the third order differential equation with the damping term \[ (a_{1}(t)(a_{2}(t)x^{\prime }(t))^{\prime })^{\prime }+q(t)x^{\prime }(t)+r(t)f(x(\varphi (t)))=0 \] in the case when the corresponding second order differential equation is oscillatory.
LA - eng
KW - third order differential equation; damping term; second order oscillatory equation; positive solution; asymptotic properties; third order differential equation; damping term; second order oscillatory equation; positive solution; asymptotic property
UR - http://eudml.org/doc/196383
ER -

References

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  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. (2009) Zbl1212.34189MR2591657
  2. Baculikova, B., Elabbasy, E. M., Saker, S. H., Dzurina, J., 10.2478/s12175-008-0068-1, Math. Slovaca 58 (2008), 201-202. (2008) Zbl1174.34052MR2391214DOI10.2478/s12175-008-0068-1
  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. (2000) MR1843694
  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). (2010) Zbl1192.34073MR2587610
  5. Bartušek, M., Cecchi, M., Marini, M., 10.1006/jmaa.2000.7473, J. Math. Anal. Appl. 261 (2001), 72-84. (2001) Zbl0995.34025MR1850957DOI10.1006/jmaa.2000.7473
  6. Cecchi, M., Došlá, Z., Marini, M., 10.1006/jmaa.1998.6247, J. Math. Anal. Appl. 231 (1999), 509-525. (1999) MR1669163DOI10.1006/jmaa.1998.6247
  7. Cecchi, M., Došlá, Z., Marini, M., 10.1016/S0362-546X(97)00028-X, Nonlinear Anal., Theory Methods Appl. 30 (1997), 1583-1594. (1997) MR1490081DOI10.1016/S0362-546X(97)00028-X
  8. Coles, W. J., Boundedness of solutions of two-dimensional first order differential systems, Boll. Un. Mat. Ital. 4 (1971), 225-231. (1971) Zbl0229.34027MR0293162
  9. Jaroš, J., Kusano, T., Marić, V., 10.2298/PIM0693051J, Publ. Inst. Math. Beograd 79 (2006), 51-64. (2006) MR2275338DOI10.2298/PIM0693051J
  10. Kiguradze, I., An oscillation criterion for a class of ordinary differential equations, Diff. Urav. 28 (1992), 201-214. (1992) Zbl0768.34018MR1184921
  11. Marini, M., Criteri di limitatezza per le soluzioni dell'equazione lineare del secondo ordine, Boll. Un. Mat. Ital. 11 (1975), 154-165. (1975) Zbl0332.34027MR0372326
  12. Mojsej, I., 10.1016/j.na.2007.04.001, Nonlinear Analysis 68 (2008), 3581-3591. (2008) Zbl1151.34053MR2401369DOI10.1016/j.na.2007.04.001
  13. Mojsej, I., Ohriska, J., 10.2478/s11533-006-0044-3, Central Eur. J. Math. 5 (2007), 154-16. (2007) Zbl1128.34021MR2287717DOI10.2478/s11533-006-0044-3
  14. Saker, S. H., Oscillation criteria of Hille and Nehari types for third order delay differential equations, Commun. Appl. Anal. 11 (2007), 451-468. (2007) Zbl1139.34049MR2368196
  15. Tiryaki, A., Aktas, M. F., 10.1016/j.jmaa.2006.01.001, J. Math. Anal. Appl. 325 (2007), 54-68. (2007) Zbl1110.34048MR2273028DOI10.1016/j.jmaa.2006.01.001
  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. (2007) Zbl1140.34415MR2367678

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