Oscillation criteria for certain forced second-order nonlinear differential equations with delayed argument. (English) Zbl 1093.34552

Çakmak, D.; Tiryaki, A.

Comput. Math. Appl. 49, No. 11-12, 1647-1653 (2005).

From the summary: Some new sufficient conditions for oscillation criteria are given for forced second-order nonlinear differential equations with delayed argument in the form \[ x''(t)+q(t)f(x(\tau(t)))= e(t). \] The results are based on the information only on a sequence of subintervals of \([t_0,\infty)\) rather than on the whole half-line.

MSC:

34K11

Oscillation theory of functional-differential equations

Keywords:

oscillation; second order; forced term; nonlinear differential equations; delayed argument

References:

[1]	Sun, Y.G., A note on nasr’s and Wong’s papers, J. math. anal. appl., 286, 363-367, (2003) · Zbl 1042.34096
[2]	Keener, M.S., Solutions of a certain linear nonhomogeneous second order differential equations, Appl. anal., 1, 57-63, (1971) · Zbl 0215.43802
[3]	Rainkin, S.M., Oscillation theorems for second order nonhomogeneous linear differential equations, J. math. anal. appl., 53, 550-553, (1976) · Zbl 0328.34033
[4]	Skidmore, A.; Leighton, W., On the differential equation y″ + p(x)y = f(x), J. math. anal. appl., 43, 46-55, (1973) · Zbl 0287.34031
[5]	Skidmore, A.; Bowers, J.J., Oscillatory behavior of solutions of y″ + p(x)y = f(x), J. math. anal. appl., 49, 317-323, (1975) · Zbl 0312.34025
[6]	Teufel, H., Forced second order nonlinear oscillations, J. math. anal. appl., 40, 148-152, (1972) · Zbl 0211.12001
[7]	Kartsatos, A.G., On the maintenance of oscillations of nth-order equations under the effect of a small forcing term, J. differential equations, 10, 355-363, (1971) · Zbl 0211.11902
[8]	Kartsatos, A.G., Maintenance of oscillations under the effect of a periodic forcing term, (), 377-383 · Zbl 0234.34040
[9]	Nasr, A.H., Necessary and sufficient conditions for the oscillation of forced nonlinear second order differential equations with delayed argument, J. math. anal. appl., 212, 51-59, (1997) · Zbl 0884.34075
[10]	Wong, J.S.W., Second order nonlinear forced oscillations, SIAM J. math. anal., 19, 667-675, (1988) · Zbl 0655.34023
[11]	El-Sayed, M.A., An oscillation criterion for a forced second order linear differential equation, (), 813-817 · Zbl 0777.34023
[12]	Nasr, A.H., Sufficient conditions for the oscillation of forced superlinear second order differential equations with oscillatory potential, (), 123-125 · Zbl 0891.34038
[13]	Wong, J.S.W., Oscillation criteria for a forced second order linear differential equation, J. math. anal. appl., 231, 235-240, (1999) · Zbl 0922.34029
[14]	Agarwal, R.P.; Grace, S.R., Second order nonlinear forced oscillations, Dynam. systems appl., 10, 455-464, (2001) · Zbl 1021.34027
[15]	Li, W.T.; Cheng, S.S., An oscillation criterion for nonhomogeneous half-linear differential equations, Appl. math. lett., 15, 3, 259-263, (2002) · Zbl 1023.34029
[16]	Çakmak, D.; Tiryaki, A., Oscillation criteria for certain forced second-order nonlinear differential equations, Appl. math. lett., 17, 3, 275-279, (2004) · Zbl 1061.34017
[17]	Wong, J.S.W., On kamenev-type oscillation theorems for second order differential equations with damping, J. math. anal. appl., 258, 244-257, (2001) · Zbl 0987.34024
[18]	Tiryaki, A.; Çakmak, D.; Ayanlar, B., On the oscillation of certain second order nonlinear differential equations, J. math. anal. appl., 281, 565-574, (2003) · Zbl 1030.34033