Maintenance of oscillations under the effect of a periodic forcing term
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- by Athanassios G. Kartsatos PDF
- Proc. Amer. Math. Soc. 33 (1972), 377-383 Request permission
Abstract:
A necessary and sufficient condition is given for the oscillation of all solutions of the differential equation \[ {x^{(n)}} + P(t,x,xβ, \cdots ,{x^{(n - 1)}}) = Q(t)\] where ${x_1}P(t,{x_1},{x_2}, \cdots ,{x_n}) > 0$ for every ${x_1} \ne 0$, and Q is a continuous periodic function. This result answers a question recently raised by J. S. W. Wong. It is also shown that a well-known sufficient condition for the existence of at least one nonoscillatory solution of the unperturbed equation guarantees, for a large class of equations, the nonexistence of bounded oscillatory solutions.References
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- 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), 355β363. MR 288358, DOI 10.1016/0022-0396(71)90058-1
- Gerald H. Ryder and David V. V. Wend, Oscillation of solutions of certain ordinary differential equations of $n\textrm {th}$ order, Proc. Amer. Math. Soc. 25 (1970), 463β469. MR 261091, DOI 10.1090/S0002-9939-1970-0261091-5
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 33 (1972), 377-383
- MSC: Primary 34C10
- DOI: https://doi.org/10.1090/S0002-9939-1972-0330622-0
- MathSciNet review: 0330622