Oscillatory and non-oscillatory criteria for linear four-dimensional Hamiltonian systems

Gevorg A. Grigorian

Mathematica Bohemica (2021)

  • Volume: 146, Issue: 3, page 289-304
  • ISSN: 0862-7959

Abstract

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The Riccati equation method is used to study the oscillatory and non-oscillatory behavior of solutions of linear four-dimensional Hamiltonian systems. One oscillatory and three non-oscillatory criteria are proved. Examples of the obtained results are compared with some well known ones.

How to cite

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Grigorian, Gevorg A.. "Oscillatory and non-oscillatory criteria for linear four-dimensional Hamiltonian systems." Mathematica Bohemica 146.3 (2021): 289-304. <http://eudml.org/doc/298203>.

@article{Grigorian2021,
abstract = {The Riccati equation method is used to study the oscillatory and non-oscillatory behavior of solutions of linear four-dimensional Hamiltonian systems. One oscillatory and three non-oscillatory criteria are proved. Examples of the obtained results are compared with some well known ones.},
author = {Grigorian, Gevorg A.},
journal = {Mathematica Bohemica},
keywords = {Riccati equation; oscillation; non-oscillation; conjoined (prepared; preferred) solution; Liouville's formula},
language = {eng},
number = {3},
pages = {289-304},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Oscillatory and non-oscillatory criteria for linear four-dimensional Hamiltonian systems},
url = {http://eudml.org/doc/298203},
volume = {146},
year = {2021},
}

TY - JOUR
AU - Grigorian, Gevorg A.
TI - Oscillatory and non-oscillatory criteria for linear four-dimensional Hamiltonian systems
JO - Mathematica Bohemica
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 146
IS - 3
SP - 289
EP - 304
AB - The Riccati equation method is used to study the oscillatory and non-oscillatory behavior of solutions of linear four-dimensional Hamiltonian systems. One oscillatory and three non-oscillatory criteria are proved. Examples of the obtained results are compared with some well known ones.
LA - eng
KW - Riccati equation; oscillation; non-oscillation; conjoined (prepared; preferred) solution; Liouville's formula
UR - http://eudml.org/doc/298203
ER -

References

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  1. Al-Dosary, K. I., Abdullah, H. K., Hussein, D., Short note on oscillation of matrix Hamiltonian systems, Yokohama Math. J. 50 (2003), 23-30. (2003) Zbl1062.34032MR2052143
  2. Butler, G. J., Erbe, L. H., Mingarelli, A. B., 10.1090/S0002-9947-1987-0896022-5, Trans. Am. Math. Soc. 303 (1987), 263-282. (1987) Zbl0648.34031MR0896022DOI10.1090/S0002-9947-1987-0896022-5
  3. Byers, R., Harris, B. J., Kwong, M. K., 10.1016/0022-0396(86)90117-8, J. Differ. Equations 61 (1986), 164-177. (1986) Zbl0609.34042MR0823400DOI10.1016/0022-0396(86)90117-8
  4. Chen, S., Zheng, Z., 10.1016/S0898-1221(03)90148-9, Comput. Math. Appl. 46 (2003), 855-862. (2003) Zbl1049.34038MR2020444DOI10.1016/S0898-1221(03)90148-9
  5. Erbe, L. H., Kong, Q., Ruan, S., 10.1090/S0002-9939-1993-1154244-0, Proc. Am. Math. Soc. 117 (1993), 957-962. (1993) Zbl0777.34024MR1154244DOI10.1090/S0002-9939-1993-1154244-0
  6. Grigoryan, G. A., 10.1134/S0012266111090023, Differ. Equ. 47 (2011), 1237-1252 translation from Differ. Uravn. 47 2011 1225-1240. (2011) Zbl1244.34051MR2918496DOI10.1134/S0012266111090023
  7. Grigoryan, G. A., 10.3103/S1066369X12110023, Russ. Math. 56 (2012), 17-30 translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2012 2012 20-35. (2012) Zbl1270.34062MR3137099DOI10.3103/S1066369X12110023
  8. Grigoryan, G. A., 10.1134/S0012266115030015, Differ. Equ. 51 (2015), 283-292 translation from Differ. Uravn. 51 2015 283-292. (2015) Zbl1344.34064MR3373201DOI10.1134/S0012266115030015
  9. Grigorian, G. A., 10.7494/OpMath.2016.36.5.589, Opusc. Math. 36 (2016), 589-601. (2016) Zbl1360.34075MR3520801DOI10.7494/OpMath.2016.36.5.589
  10. Grigorian, G. A., 10.1216/RMJ-2017-47-5-1497, Rocky Mt. J. Math. 47 (2017), 1497-1524. (2017) Zbl1378.34052MR3705762DOI10.1216/RMJ-2017-47-5-1497
  11. Grigorian, G. A., 10.5817/AM2018-4-189, Arch. Math., Brno 54 (2018), 189-203. (2018) Zbl06997350MR3887360DOI10.5817/AM2018-4-189
  12. Kumary, I. S., Umamaheswaram, S., 10.1006/jdeq.1999.3746, J. Differ. Equations 165 (2000), 174-198. (2000) Zbl0970.34025MR1771793DOI10.1006/jdeq.1999.3746
  13. Li, L., Meng, F., Zheng, Z., Oscillation results related to integral averaging technique for linear Hamiltonian systems, Dyn. Syst. Appl. 18 (2009), 725-736. (2009) Zbl1208.34040MR2562259
  14. Meng, F., Mingarelli, A. B., 10.1090/S0002-9939-02-06614-5, Proc. Am. Math. Soc. 131 (2003), 897-904. (2003) Zbl1008.37032MR1937428DOI10.1090/S0002-9939-02-06614-5
  15. Mingarelli, A. B., 10.1090/S0002-9939-1981-0614884-3, Proc. Am. Math. Soc. 82 (1981), 593-598. (1981) Zbl0487.34030MR0614884DOI10.1090/S0002-9939-1981-0614884-3
  16. Sun, Y. G., 10.1016/S0022-247X(03)00053-2, J. Math. Anal. Appl. 279 (2003), 651-658. (2003) Zbl1032.34032MR1974052DOI10.1016/S0022-247X(03)00053-2
  17. Wang, Q., 10.1007/PL00000448, Arch. Math. 76 (2001), 385-390. (2001) Zbl0989.34024MR1824258DOI10.1007/PL00000448
  18. Yang, Q., Mathsen, R., Zhu, S., 10.1016/S0022-0396(02)00172-9, J. Differ. Equations 190 (2003), 306-329. (2003) Zbl1032.34033MR1970965DOI10.1016/S0022-0396(02)00172-9
  19. Zheng, Z., 10.1016/j.jmaa.2006.10.034, J. Math. Anal. Appl. 332 (2007), 236-245. (2007) Zbl1124.34021MR2319657DOI10.1016/j.jmaa.2006.10.034
  20. Zheng, Z., Zhu, S., Hartman type oscillation criteria for linear matrix Hamiltonian systems, Dyn. Syst. Appl. 17 (2008), 85-96. (2008) Zbl1203.34059MR2433892

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