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ISSN 1088-6826(e) ISSN 0002-9939(p)

Sufficient conditions for the oscillation of forced super-linear second order differential equations with oscillatory potential

Author(s): A. H. Nasr
Journal: Proc. Amer. Math. Soc. 126 (1998), 123-125.
MSC (1991): Primary 34C15
MathSciNet review: 1451823
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Abstract | References | Similar articles | Additional information

Abstract: In the case of oscillatory potentials, we give sufficient conditions for the oscillation of the forced super-linear equation

$\begin{displaymath}x''(t)+a(t)|x(t)|^{\nu }\operatorname{sgn} x(t)=g(t).\end{displaymath}$

This answers a question raised by J. S. W. Wong.

References:

1.: E. F. Beckenbach and R. Bellman, Inequalities, ``Springer-Verlag'', Berlin, 1961. MR 28:1266
2.: M. A. El-Sayed, An oscillation criterion for forced second order linear differential equation, Proc. Amer. Math. Soc. 118, 3 (1993), 813-817. MR 93i:34058
3.: A. G. Kartsatos, On the maintenance of oscillation of n-th order equations under the effect of a small forcing term, J. Diff. Equations 10 (1971), 355-363. MR 44:5556
4.: A. G. Kartsatos, Maintenance of oscillations under the effect of a periodic forcing term, Proc. Amer. Math. Soc. 33 (1972), 377-382. MR 48:8959
5.: V. Komkov, On boundedness and oscillation of the differential equation $x''-A(t)\mathbf{g}(\mathbf{x})=\mathbf{f}(t)$ in $\mathbb{R}^{n}$ , SIAM J. Appl. Math. 22 (1972), 561-568. MR 47:554
6.: S. M. Rankin, Oscillation theorems for second order nonhomogeneous linear differential equations, J. Math. Anal. Appl. 53 (1976), 550-553. MR 53:6007
7.: J. S. W. Wong, Second order nonlinear forced oscillations, SIAM J. Math. Anal. 19, 3 (1988), 667-675. MR 89e:34065

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