Oscillation of fourth-order quasilinear differential equations

Tongxing Li; Yuriy V. Rogovchenko; Chenghui Zhang

Mathematica Bohemica (2015)

  • Volume: 140, Issue: 4, page 405-418
  • ISSN: 0862-7959

Abstract

top
We study oscillatory behavior of a class of fourth-order quasilinear differential equations without imposing restrictive conditions on the deviated argument. This allows applications to functional differential equations with delayed and advanced arguments, and not only these. New theorems are based on a thorough analysis of possible behavior of nonoscillatory solutions; they complement and improve a number of results reported in the literature. Three illustrative examples are presented.

How to cite

top

Li, Tongxing, Rogovchenko, Yuriy V., and Zhang, Chenghui. "Oscillation of fourth-order quasilinear differential equations." Mathematica Bohemica 140.4 (2015): 405-418. <http://eudml.org/doc/271833>.

@article{Li2015,
abstract = {We study oscillatory behavior of a class of fourth-order quasilinear differential equations without imposing restrictive conditions on the deviated argument. This allows applications to functional differential equations with delayed and advanced arguments, and not only these. New theorems are based on a thorough analysis of possible behavior of nonoscillatory solutions; they complement and improve a number of results reported in the literature. Three illustrative examples are presented.},
author = {Li, Tongxing, Rogovchenko, Yuriy V., Zhang, Chenghui},
journal = {Mathematica Bohemica},
keywords = {oscillation; quasilinear functional differential equation; delayed argument; advanced argument},
language = {eng},
number = {4},
pages = {405-418},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Oscillation of fourth-order quasilinear differential equations},
url = {http://eudml.org/doc/271833},
volume = {140},
year = {2015},
}

TY - JOUR
AU - Li, Tongxing
AU - Rogovchenko, Yuriy V.
AU - Zhang, Chenghui
TI - Oscillation of fourth-order quasilinear differential equations
JO - Mathematica Bohemica
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 140
IS - 4
SP - 405
EP - 418
AB - We study oscillatory behavior of a class of fourth-order quasilinear differential equations without imposing restrictive conditions on the deviated argument. This allows applications to functional differential equations with delayed and advanced arguments, and not only these. New theorems are based on a thorough analysis of possible behavior of nonoscillatory solutions; they complement and improve a number of results reported in the literature. Three illustrative examples are presented.
LA - eng
KW - oscillation; quasilinear functional differential equation; delayed argument; advanced argument
UR - http://eudml.org/doc/271833
ER -

References

top
  1. 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 Marcel Dekker, New York (2004). (2004) Zbl1068.34002MR2084730
  2. Agarwal, R. P., Grace, S. R., Manojlovic, J. V., 10.1016/j.mcm.2005.11.015, Math. Comput. Modelling 44 163-187 (2006). (2006) Zbl1137.34031MR2230441DOI10.1016/j.mcm.2005.11.015
  3. Agarwal, R. P., Grace, S. R., O'Regan, D., Oscillation Theory for Difference and Functional Differential Equations, Kluwer Academic Publishers, Dordrecht (2000). (2000) Zbl0954.34002MR1774732
  4. Agarwal, R. P., Grace, S. R., O'Regan, D., 10.1006/jmaa.2001.7571, J. Math. Anal. Appl. 262 601-622 (2001). (2001) Zbl0997.34060MR1859327DOI10.1006/jmaa.2001.7571
  5. Agarwal, R. P., Grace, S. R., O'Regan, D., 10.1007/s11253-007-0021-4, Ukr. Mat. J. 59 315-342 (2007). (2007) Zbl1150.34545MR2359966DOI10.1007/s11253-007-0021-4
  6. Bartušek, M., Cecchi, M., Došlá, Z., Marini, M., Fourth-order differential equation with deviating argument, Abstr. Appl. Anal. 2012 Article ID 185242, 17 pages (2012). (2012) Zbl1244.34089MR2898056
  7. Grace, S. R., Agarwal, R. P., Graef, J. R., 10.1007/s12190-008-0158-9, J. Appl. Math. Comput. 30 75-88 (2009). (2009) Zbl1188.34085MR2496603DOI10.1007/s12190-008-0158-9
  8. Grace, S. R., Agarwal, R. P., Pinelas, S., On the oscillations of fourth order functional differential equations, Commun. Appl. Anal. 13 93-103 (2009). (2009) Zbl1180.34064MR2514990
  9. Hasanbulli, M., Rogovchenko, Yu. V., 10.1016/j.na.2007.06.025, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 69 1208-1218 (2008). (2008) Zbl1157.34057MR2426686DOI10.1016/j.na.2007.06.025
  10. Kamo, K.-I., Usami, H., Oscillation theorems for fourth-order quasilinear ordinary differential equations, Stud. Sci. Math. Hung. 39 385-406 (2002). (2002) Zbl1026.34054MR1956947
  11. Kamo, K., Usami, H., 10.1007/s10474-011-0127-x, Acta Math. Hung. 132 207-222 (2011). (2011) Zbl1249.34111MR2818904DOI10.1007/s10474-011-0127-x
  12. Kiguradze, I. T., Chanturia, T. A., 10.1007/978-94-011-1808-8, Mathematics and Its Applications (Soviet Series) 89 Kluwer Academic Publishers, Dordrecht (1993), translated from the Russian. (1993) Zbl0782.34002MR1220223DOI10.1007/978-94-011-1808-8
  13. Kitamura, Y., Kusano, T., 10.1090/S0002-9939-1980-0548086-5, Proc. Am. Math. Soc. 78 64-68 (1980). (1980) Zbl0433.34051MR0548086DOI10.1090/S0002-9939-1980-0548086-5
  14. Kusano, T., Manojlović, J., Tanigawa, T., 10.1216/RMJ-2011-41-1-249, Rocky Mt. J. Math. 41 249-274 (2011). (2011) Zbl1232.34053MR2845944DOI10.1216/RMJ-2011-41-1-249
  15. Ladde, G. S., Lakshmikantham, V., Zhang, B. G., Oscillation Theory of Differential Equations with Deviating Arguments, Monographs and Textbooks in Pure and Applied Mathematics 110 Marcel Dekker, New York (1987). (1987) Zbl0832.34071MR1017244
  16. Li, T., Thandapani, E., Tang, S., Oscillation theorems for fourth-order delay dynamic equations on time scales, Bull. Math. Anal. Appl. 3 190-199 (2011). (2011) Zbl1314.34182MR2955359
  17. Onose, H., 10.5036/bfsiu1968.11.57, Bull. Fac. Sci., Ibaraki Univ., Ser. A 11 57-63 (1979). (1979) Zbl0416.34064MR0536902DOI10.5036/bfsiu1968.11.57
  18. Onose, H., 10.1007/BF02413181, Ann. Mat. Pura Appl. (4) 119 259-272 (1979). (1979) Zbl0412.34067MR0551229DOI10.1007/BF02413181
  19. Philos, Ch., A new criterion for the oscillatory and asymptotic behavior of delay differential equations, Bull. Acad. Pol. Sci., Sér. Sci. Math. 29 367-370 (1981). (1981) Zbl0482.34056MR0640329
  20. Wu, F., 10.1016/j.jmaa.2011.11.061, J. Math. Anal. Appl. 389 632-646 (2012). (2012) Zbl1244.34054MR2876527DOI10.1016/j.jmaa.2011.11.061
  21. Zhang, C., Agarwal, R. P., Bohner, M., Li, T., 10.1016/j.aml.2012.08.004, Appl. Math. Lett. 26 179-183 (2013). (2013) Zbl1263.34094MR2994606DOI10.1016/j.aml.2012.08.004
  22. Zhang, C., Li, T., Agarwal, R. P., Bohner, M., 10.1016/j.aml.2012.04.018, Appl. Math. Lett. 25 2058-2065 (2012). (2012) Zbl1260.34168MR2967789DOI10.1016/j.aml.2012.04.018
  23. Zhang, C., Li, T., Sun, B., Thandapani, E., 10.1016/j.aml.2011.04.015, Appl. Math. Lett. 24 1618-1621 (2011). (2011) Zbl1223.34095MR2803721DOI10.1016/j.aml.2011.04.015

NotesEmbed ?

top

You must be logged in to post comments.