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Boundedness of solutions of the third order differential equation with oscillatory restoring and forcing terms. (English) Zbl 0608.34039

Sufficient conditions for the boundedness of all solutions of the equation \(x\prime''+ax''+bx'+h(x)=p(t)\) are given by means of the well- known Cauchy formula in order that these solutions be oscillatory as well. It is shown that such a requirement is satisfied when the distance between the roots of the restoring term is large enough.

MSC:

34C11 Growth and boundedness of solutions to ordinary differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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References:

[1] W. A. Coppel: Stability and Asymptotic Behavior of Differential Equations. D. C. Heath, Boston, 1975. · Zbl 0154.09301
[2] J. Andres: Asymptotic properties of solutions of a certain third order differential equation with the oscillatory restoring term. to appear. · Zbl 0701.34070
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