Sufficient conditions for the oscillation of forced super-linear second order differential equations with oscillatory potential. (English) Zbl 0891.34038

Nasr, A. H.

Proc. Am. Math. Soc. 126, No. 1, 123-125 (1998).

Summary: In the case of oscillatory potentials, we give sufficient conditions for the oscillation of the forced super-linear equation \[ x''(t)+a(t)|x(t)|^{\nu}\text{ sgn } x(t)=g(t). \] This answers a question raised by J. S. W. Wong [SIAM J. Math. Anal. 19, No. 3, 667-675 (1988; Zbl 0655.34023)].

MSC:

34C15

Nonlinear oscillations and coupled oscillators for ordinary differential equations

Keywords:

nonlinear second order differential equations; oscillation

Citations:

Zbl 0655.34023

References:

[1]	Edwin F. Beckenbach and Richard Bellman, Inequalities, Ergebnisse der Mathematik und ihrer Grenzgebiete, N. F., Bd. 30, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1961. · Zbl 0097.26502
[2]	M. A. El-Sayed, An oscillation criterion for a forced second order linear differential equation, Proc. Amer. Math. Soc. 118 (1993), no. 3, 813 – 817. · Zbl 0777.34023
[3]	Athanassios G. Kartsatos, On the maintenance of oscillations of \?th order equations under the effect of a small forcing term, J. Differential Equations 10 (1971), 355 – 363. · Zbl 0216.11504
[4]	Athanassios G. Kartsatos, Maintenance of oscillations under the effect of a periodic forcing term, Proc. Amer. Math. Soc. 33 (1972), 377 – 383. · Zbl 0234.34040
[5]	V. Komkov, On boundedness and oscillation of the differential equation \?\(^{\prime}\)\(^{\prime}\)+\?(\?)\?(\?)=\?(\?) in \?\(^{n}\), SIAM J. Appl. Math. 22 (1972), 561 – 568. · Zbl 0223.34029
[6]	Samuel M. Rankin III, Oscillation theorems for second-order nonhomogeneous linear differential equations, J. Math. Anal. Appl. 53 (1976), no. 3, 550 – 553. · Zbl 0328.34033
[7]	James S. W. Wong, Second order nonlinear forced oscillations, SIAM J. Math. Anal. 19 (1988), no. 3, 667 – 675. · Zbl 0655.34023