Sufficient conditions for the oscillation of forced super-linear second order differential equations with oscillatory potential
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- by A. H. Nasr PDF
- Proc. Amer. Math. Soc. 126 (1998), 123-125 Request permission
Abstract:
In the case of oscillatory potentials, we give sufficient conditions for the oscillation of the forced super-linear equation \[ x''(t)+a(t)|x(t)|^{\nu }\operatorname {sgn} x(t)=g(t).\] This answers a question raised by J. S. W. Wong.References
- Edwin F. Beckenbach and Richard Bellman, Inequalities, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 30, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1961. MR 0158038, DOI 10.1007/978-3-642-64971-4
- 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. MR 1154243, DOI 10.1090/S0002-9939-1993-1154243-9
- Athanassios G. Kartsatos, On the maintenance of oscillations of $n$th order equations under the effect of a small forcing term, J. Differential Equations 10 (1971), 355–363. MR 288358, DOI 10.1016/0022-0396(71)90058-1
- Athanassios G. Kartsatos, Maintenance of oscillations under the effect of a periodic forcing term, Proc. Amer. Math. Soc. 33 (1972), 377–383. MR 330622, DOI 10.1090/S0002-9939-1972-0330622-0
- V. Komkov, On boundedness and oscillation of the differential equation $\textbf {x}^{\prime \prime }+A(t)\textbf {g}(\textbf {x})=\textbf {f}(t)$ in $R^{n}$, SIAM J. Appl. Math. 22 (1972), 561–568. MR 311992, DOI 10.1137/0122051
- Samuel M. Rankin III, Oscillation theorems for second-order nonhomogeneous linear differential equations, J. Math. Anal. Appl. 53 (1976), no. 3, 550–553. MR 402186, DOI 10.1016/0022-247X(76)90091-3
- James S. W. Wong, Second order nonlinear forced oscillations, SIAM J. Math. Anal. 19 (1988), no. 3, 667–675. MR 937477, DOI 10.1137/0519047
Additional Information
- A. H. Nasr
- Affiliation: Department of Mathematics, Ain Shans University College for Girls, Asma Fahmi St. Heliopolis, Cairo, Egypt
- Received by editor(s): March 19, 1996
- Additional Notes: The author is deceased
- Communicated by: Hal L. Smith
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 123-125
- MSC (1991): Primary 34C15
- DOI: https://doi.org/10.1090/S0002-9939-98-04354-8
- MathSciNet review: 1451823