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Oscillation of second-order nonlinear ODE with damping. (English) Zbl 1122.34027
The authors consider the differential equation $$ (r(t)k_1(x(t),x'(t)))'+p(t)k_2(x(t),x'(t))x'(t)+ q(t)f(x(t))=0,\qquad t\geq t_0,\tag{1} $$ where $t_0$ is a fixed real number, $r\in C([t_0,+\infty);(0,+\infty))$, $p,q\in C([t_0,+\infty);\Bbb R)$, $f\in C(\Bbb R;\Bbb R)$, and $k_1,k_2\in C(\Bbb R^2;\Bbb R)$. Conditions are established guaranteeing that $(1)$ is oscillatory.

34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
Full Text: DOI
[1] Grace, S. R.: Oscillation theorems for nonlinear differential equations of second order. J. math. Anal. appl. 171, 220-241 (1992) · Zbl 0767.34017
[2] Grace, S. R.; Lalli, B. S.: Integral averaging techniques for the oscillation of second order nonlinear differential equations. J. math. Anal. appl. 149, 277-311 (1990) · Zbl 0697.34040
[3] Kirane, M.; Rogovchenko, Y. V.: Oscillation results for second order damped differential equation with nonmonotonous nonlinearity. J. math. Anal. appl. 250, 118-138 (2000) · Zbl 1008.34029
[4] Kirane, M.; Rogovchenko, Y. V.: On oscillatory of nonlinear second order differential equation with damping term. Appl. math. Comput. 117, 177-192 (2001) · Zbl 1035.34019
[5] Rogovchenko, Y. V.: Oscillation theorems for second order differential equations with damping. Nonlinear anal. 41, 1005-1028 (2000) · Zbl 0972.34022
[6] Yan, J.: Oscillation theorems for second order linear differential equations with damping. Proc. amer. Math. soc. 98, 276-282 (1986) · Zbl 0622.34027
[7] Li, W. T.; Agarwal, R. P.: Integral oscillation criteria for second order nonlinear differential equations with damping. Comput. math. Appl. 40, 217-230 (2000) · Zbl 0959.34026
[8] Li, W. T.: Interval oscillation of second-order half-linear functional differential equations. Appl. math. Comput. 155, 451-468 (2004) · Zbl 1061.34048
[9] Rogovchenko, S. P.; Rogovchenko, Y. V.: Oscillation of second order differential equations with damping. Dynam. contin. Discrete impuls. Systems ser. A 10, 447-461 (2003) · Zbl 1048.34071
[10] Rogovchenko, S. P.; Rogovchenko, Y. V.: Oscillation theorems for differential equation with a nonlinear damping term. J. math. Anal. appl. 279, 121-134 (2003) · Zbl 1027.34040
[11] Mustafa, O. G.; Rogovchenko, S. P.; Rogovchenko, Y. V.: On oscillation of nonlinear second-order differential equations with damping term. J. math. Anal. appl. 298, 604-620 (2004) · Zbl 1061.34021
[12] Ayanlar, B.; Tiryaki, A.: Oscillation theorems for nonlinear second order differential equations with damping. Acta math. Hungar. 89, No. 1-2, 1-13 (2000) · Zbl 0973.34021
[13] Tiryaki, A.; &ccedil, D.; Akmak; Ayanlar, B.: On the oscillation of certain second-order nonlinear differential equations. J. math. Anal. appl. 281, 565-574 (2003) · Zbl 1030.34033
[14] Tiryaki, A.; Zafer, A.: Interval oscillation of a general class of second-order nonlinear differential equations with nonlinear damping. Nonlinear anal. 60, 49-63 (2005) · Zbl 1064.34021
[15] &ccedil, D.; Akmak; Tiryaki, A.: Oscillation criteria for certain forced second-order nonlinear differential equations. Appl. math. Lett. 17, 275-279 (2004) · Zbl 1061.34017
[16] Wang, Q. R.: Oscillation criteria for nonlinear second order damped differential equations. Acta math. Hungar. 102, No. 1 -- 2, 117-139 (2004) · Zbl 1052.34040