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.


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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[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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