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Oscillation criteria for forced second-order nonlinear differential equations with damping. (English) Zbl 1167.34325
The authors investigate oscillations of a class of forced second-order differential equations with nonlinear damping terms. Some new interval oscillation criteria for the equations are obtained via using a classical variational principle and an averaging technique. Also, some examples which improve and extend some known results are included.

##### MSC:
 34C10 Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
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##### References:
 [1] Yang, Q.: Interval oscillation criteria for a forced second-order nonlinear ordinary differential equations with oscillatory potential, Appl. math. Comput. 135, 49-64 (2003) · Zbl 1030.34034 · doi:10.1016/S0096-3003(01)00307-1 [2] Cakmak, D.; Tiryaki, A.: Oscillation criteria for certain forced second order nonlinear differential equations, Appl. math. Lett. 17, 275-279 (2004) · Zbl 1061.34017 · doi:10.1016/S0893-9659(04)90063-8 [3] Jiang, Fangcui; Meng, Fanwei: New oscillation criteria for a class of second-order nonlinear forced differential equations, J. math. Anal. appl. 336, No. 2, 1476-1485 (2007) · Zbl 1128.34018 · doi:10.1016/j.jmaa.2007.02.055 [4] El-Sayed, M. A.: An oscillation criteria for a forced second-order linear differential equations, Proc. amer. Math. soc. 118, No. 3, 813-817 (1993) · Zbl 0777.34023 · doi:10.2307/2160125 [5] Wong, J. S. W.: Oscillation criteria for a forced second-order linear differential equations, J. math. Anal. appl. 231, 235-240 (1999) · Zbl 0922.34029 · doi:10.1006/jmaa.1998.6259 [6] Keener, M. S.: Solution of a certain linear nonhomogeneous second-order differential equation, Appl. anal. 1, 57-63 (1971) · Zbl 0215.43802 · doi:10.1080/00036817108839006 [7] Wong, J. S. W.: Second-order nonlinear forced oscillations, SIAM J. Math. anal. 19, 667-675 (1988) · Zbl 0655.34023 · doi:10.1137/0519047 [8] Rankin, S. M.: Oscillation theorems for second-order nonhomogeneous linear differential equation, J. math. Anal. appl. 53, 550-553 (1976) · Zbl 0328.34033 · doi:10.1016/0022-247X(76)90091-3 [9] Hardy, G. H.; Littlewood, J. E.; Polya, G.: Inequalities, (1988) [10] Kong, Q.: Interval criteria for oscillation of second order linear ordinary differential equations, J. math. Anal. appl. 229, 258-270 (1999) · Zbl 0924.34026 · doi:10.1006/jmaa.1998.6159 [11] Li, W. T.: Interval criteria for oscillation of second order half-linear ordinary differential equations, Acta math. Sinica 43, No. 3, 509-516 (2002) · Zbl 1018.34036 [12] Zhao, Xueqin; Meng, Fanwei: Oscillation of second-order nonlinear ODE with damping, Appl. math. Comput. 182, 1861-1871 (2006) · Zbl 1122.34027 · doi:10.1016/j.amc.2006.06.022 [13] Shi, Wenying: Interval oscillation criteria for a forced second-order differential equations with nonlinear damping, Math. comput. Modelling 43, 170-177 (2006) · Zbl 1102.34022 · doi:10.1016/j.mcm.2005.09.024 [14] Skidmore, A.; Leighton, W.: On the equation y”+$p(x)y=f(x)$, J. math. Anal. appl. 43, 46-55 (1973) · Zbl 0287.34031 [15] Skidmore, A.; Bowers, J. J.: Oscillation behavior of solutions of y”+$p(x)y=f(x)$, J. math. Anal. appl. 49, 317-323 (1975) · Zbl 0312.34025 · doi:10.1016/0022-247X(75)90183-3