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Title: Oscillation of fourth-order quasilinear differential equations (English)
Author: Li, Tongxing
Author: Rogovchenko, Yuriy V.
Author: Zhang, Chenghui
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 140
Issue: 4
Year: 2015
Pages: 405-418
Summary lang: English
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Category: math
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Summary: 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. (English)
Keyword: oscillation
Keyword: quasilinear functional differential equation
Keyword: delayed argument
Keyword: advanced argument
MSC: 34K11
idZBL: Zbl 06537673
idMR: MR3432542
DOI: 10.21136/MB.2015.144459
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Date available: 2015-11-17T20:46:13Z
Last updated: 2020-07-29
Stable URL: http://hdl.handle.net/10338.dmlcz/144459
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Reference: [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). Zbl 1068.34002, MR 2084730
Reference: [2] Agarwal, R. P., Grace, S. R., Manojlovic, J. V.: Oscillation criteria for certain fourth order nonlinear functional differential equations.Math. Comput. Modelling 44 163-187 (2006). Zbl 1137.34031, MR 2230441, 10.1016/j.mcm.2005.11.015
Reference: [3] Agarwal, R. P., Grace, S. R., O'Regan, D.: Oscillation Theory for Difference and Functional Differential Equations.Kluwer Academic Publishers, Dordrecht (2000). Zbl 0954.34002, MR 1774732
Reference: [4] Agarwal, R. P., Grace, S. R., O'Regan, D.: Oscillation criteria for certain $n$th order differential equations with deviating arguments.J. Math. Anal. Appl. 262 601-622 (2001). Zbl 0997.34060, MR 1859327, 10.1006/jmaa.2001.7571
Reference: [5] Agarwal, R. P., Grace, S. R., O'Regan, D.: Oscillation of certain fourth-order functional differential equations.Ukr. Mat. J. 59 315-342 (2007). Zbl 1150.34545, MR 2359966, 10.1007/s11253-007-0021-4
Reference: [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). Zbl 1244.34089, MR 2898056
Reference: [7] Grace, S. R., Agarwal, R. P., Graef, J. R.: Oscillation theorems for fourth order functional differential equations.J. Appl. Math. Comput. 30 75-88 (2009). Zbl 1188.34085, MR 2496603, 10.1007/s12190-008-0158-9
Reference: [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). Zbl 1180.34064, MR 2514990
Reference: [9] Hasanbulli, M., Rogovchenko, Yu. V.: Asymptotic behavior of nonoscillatory solutions to $n$-th order nonlinear neutral differential equations.Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 69 1208-1218 (2008). Zbl 1157.34057, MR 2426686, 10.1016/j.na.2007.06.025
Reference: [10] Kamo, K.-I., Usami, H.: Oscillation theorems for fourth-order quasilinear ordinary differential equations.Stud. Sci. Math. Hung. 39 385-406 (2002). Zbl 1026.34054, MR 1956947
Reference: [11] Kamo, K., Usami, H.: Nonlinear oscillations of fourth order quasilinear ordinary differential equations.Acta Math. Hung. 132 207-222 (2011). Zbl 1249.34111, MR 2818904, 10.1007/s10474-011-0127-x
Reference: [12] Kiguradze, I. T., Chanturia, T. A.: Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations.Mathematics and Its Applications (Soviet Series) 89 Kluwer Academic Publishers, Dordrecht (1993), translated from the Russian. Zbl 0782.34002, MR 1220223, 10.1007/978-94-011-1808-8
Reference: [13] Kitamura, Y., Kusano, T.: Oscillation of first-order nonlinear differential equations with deviating arguments.Proc. Am. Math. Soc. 78 64-68 (1980). Zbl 0433.34051, MR 0548086, 10.1090/S0002-9939-1980-0548086-5
Reference: [14] Kusano, T., Manojlović, J., Tanigawa, T.: Sharp oscillation criteria for a class of fourth order nonlinear differential equations.Rocky Mt. J. Math. 41 249-274 (2011). Zbl 1232.34053, MR 2845944, 10.1216/RMJ-2011-41-1-249
Reference: [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). Zbl 0832.34071, MR 1017244
Reference: [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). Zbl 1314.34182, MR 2955359
Reference: [17] Onose, H.: Forced oscillation for functional differential equations of fourth order.Bull. Fac. Sci., Ibaraki Univ., Ser. A 11 57-63 (1979). Zbl 0416.34064, MR 0536902, 10.5036/bfsiu1968.11.57
Reference: [18] Onose, H.: Nonlinear oscillation of fourth order functional differential equations.Ann. Mat. Pura Appl. (4) 119 259-272 (1979). Zbl 0412.34067, MR 0551229, 10.1007/BF02413181
Reference: [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). Zbl 0482.34056, MR 0640329
Reference: [20] Wu, F.: Existence of eventually positive solutions of fourth order quasilinear differential equations.J. Math. Anal. Appl. 389 632-646 (2012). Zbl 1244.34054, MR 2876527, 10.1016/j.jmaa.2011.11.061
Reference: [21] Zhang, C., Agarwal, R. P., Bohner, M., Li, T.: New results for oscillatory behavior of even-order half-linear delay differential equations.Appl. Math. Lett. 26 179-183 (2013). Zbl 1263.34094, MR 2994606, 10.1016/j.aml.2012.08.004
Reference: [22] Zhang, C., Li, T., Agarwal, R. P., Bohner, M.: Oscillation results for fourth-order nonlinear dynamic equations.Appl. Math. Lett. 25 2058-2065 (2012). Zbl 1260.34168, MR 2967789, 10.1016/j.aml.2012.04.018
Reference: [23] Zhang, C., Li, T., Sun, B., Thandapani, E.: On the oscillation of higher-order half-linear delay differential equations.Appl. Math. Lett. 24 1618-1621 (2011). Zbl 1223.34095, MR 2803721, 10.1016/j.aml.2011.04.015
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