×

Oscillation criteria for a class of second-order nonlinear differential equations with damping term. (English) Zbl 1181.34044

Summary: We investigate the differential equation
\[ (r(t)|x'(t)|^{\sigma-1}x'(t))'+p(t)|x'(t)|\sigma-1x'(t) +q(t)f(x(t))=0 \]
are investigated in this paper. By using a new method, we obtain some new sufficient conditions for the oscillation of the above equation, and some references are extended in this paper. Examples are inserted to illustrate this result.

MSC:

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] H. J. Li, “Oscillation criteria for second order linear differential equations,” Journal of Mathematical Analysis and Applications, vol. 194, no. 1, pp. 217-234, 1995. · Zbl 0872.34018 · doi:10.1006/jmaa.1995.1295
[2] W.-T. Li, “Oscillation of certain second-order nonlinear differential equations,” Journal of Mathematical Analysis and Applications, vol. 217, no. 1, pp. 1-14, 1998. · Zbl 0893.34023 · doi:10.1006/jmaa.1997.5680
[3] P. J. Y. Wong and R. P. Agarwal, “Oscillatory behavior of solutions of certain second order nonlinear differential equations,” Journal of Mathematical Analysis and Applications, vol. 198, no. 2, pp. 337-354, 1996. · Zbl 0855.34039 · doi:10.1006/jmaa.1996.0086
[4] P. J. Y. Wong and R. P. Agarwal, “The oscillation and asymptotically monotone solutions of second-order quasilinear differential equations,” Applied Mathematics and Computation, vol. 79, no. 2-3, pp. 207-237, 1996. · Zbl 0872.34020 · doi:10.1016/0096-3003(95)00267-7
[5] W. Li and J. R. Yan, “Oscillation criteria for second order superlinear differential equations,” Indian Journal of Pure and Applied Mathematics, vol. 28, no. 6, pp. 735-740, 1997. · Zbl 0880.34033
[6] A. Tiryaki and A. Zafer, “Oscillation criteria for second order nonlinear differential equations with damping,” Turkish Journal of Mathematics, vol. 24, no. 2, pp. 185-196, 2000. · Zbl 0977.34027
[7] J. S. W. Wong, “On Kamenev-type oscillation theorems for second-order differential equations with damping,” Journal of Mathematical Analysis and Applications, vol. 258, no. 1, pp. 244-257, 2001. · Zbl 0987.34024 · doi:10.1006/jmaa.2000.7376
[8] X. Yang, “Oscillation criteria for nonlinear differential equations with damping,” Applied Mathematics and Computation, vol. 136, no. 2-3, pp. 549-557, 2003. · Zbl 1034.34041 · doi:10.1016/S0096-3003(02)00079-6
[9] O. G. Mustafa, S. P. Rogovchenko, and Yu. V. Rogovchenko, “On oscillation of nonlinear second-order differential equations with damping term,” Journal of Mathematical Analysis and Applications, vol. 298, no. 2, pp. 604-620, 2004. · Zbl 1061.34021 · doi:10.1016/j.jmaa.2004.05.029
[10] W.-T. Li and P. Zhao, “Oscillation theorems for second-order nonlinear differential equations with damped term,” Mathematical and Computer Modelling, vol. 39, no. 4-5, pp. 457-471, 2004. · Zbl 1061.34020 · doi:10.1016/S0895-7177(04)90517-1
[11] Yu. V. Rogovchenko and F. Tuncay, “Oscillation criteria for second-order nonlinear differential equations with damping,” Nonlinear Analysis, vol. 69, no. 1, pp. 208-221, 2008. · Zbl 1147.34026 · doi:10.1016/j.na.2007.05.012
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.