A note on Nasr’s and Wong’s papers. (English) Zbl 1042.34096

Summary: In the case of oscillatory potentials, we give sufficient conditions for the oscillation of a forced nonlinear second-order differential equations with delayed argument of the form \[ x^{\prime\prime}(t)+ q(t)| x(\tau(t)) |^\gamma \operatorname{sgn} x(\tau(t))= f(t) \] in the linear (\(\gamma\)=1) and the superlinear (\(\gamma>1\)) case. See, A. H. Nasr [Proc. Am. Math. Soc. 126, 123–125 (1998; Zbl 0891.34038)] and {J. S. W. Wong} [J. Math. Anal. Appl. 231, 235–240 (1999; Zbl 0922.34029)].


34K11 Oscillation theory of functional-differential equations
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[1] Kartsatos, A. G., On the maintenance of oscillation of \(n\)-th order equations under the effect of a small forcing term, J. Differential Equations, 10, 355-363 (1971) · Zbl 0211.11902
[2] Kartsatos, A. G., Maintenance of oscillations under the effect of a periodic forcing term, Proc. Amer. Math. Soc., 33, 377-382 (1972) · Zbl 0234.34040
[3] El-Sayed, M. A., An oscillation criterion for a forced second order linear differential equation, Proc. Amer. Math. Soc., 118, 813-817 (1993) · Zbl 0777.34023
[4] Nasr, A. H., Sufficient conditions for the oscillation of forced super-linear second order differential equations with oscillatory potential, Proc. Amer. Math. Soc., 126, 123-125 (1998) · Zbl 0891.34038
[5] 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
[6] Keener, M. S., Solutions of a certain linear nonhomogeneous second order differential equations, Appl. Anal., 1, 57-63 (1971) · Zbl 0215.43802
[7] Teufel, H., Forced second order nonlinear oscillations, J. Math. Anal. Appl., 40, 148-152 (1972) · Zbl 0211.12001
[8] 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
[9] 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
[10] Rainikin, S. M., Oscillation theorems for second order nonhomogeneous linear differential equations, J. Math. Anal. Appl., 53, 550-553 (1976) · Zbl 0328.34033
[11] Wong, J. S.W., Second order nonlinear forced oscillations, SIAM J. Math. Anal., 19, 667-675 (1988) · Zbl 0655.34023
[12] 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
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