Oscillatory solutions of some perturbed second order differential equations

Details Oscillatory solutions of some perturbed second order differential equations Oscillatory solutions of some perturbed second order differential equations

2010-01-06

arxiv.org/abs/1001.0931v1

Mathematics

Classical Analysis and ODEs

Scientific paper

We discuss the occurrence of oscillatory solutions which decay to 0 as $s\to+\infty$ for a class of perturbed second order ordinary differential equations. As opposed to other results in the recent literature, the perturbation is as small as desired in terms of its improper integrals and it is independent of the coefficients of the non-oscillatory unperturbed equation. This class of equations reveals thus a new pathology in the theory of perturbed oscillations.

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