Stability implications on the asymptotic behavior of second order differential equations
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- by John M. Bownds PDF
- Proc. Amer. Math. Soc. 39 (1973), 169-172 Request permission
Abstract:
Using some basic observations from stability theory, it is shown that the classical equation $y'' + a(t)y = 0$ must have at least one solution $y(t)$ such that $\lim \sup (|y(t)| + |y’(t)|) > 0$ as $t \to \infty$. The same conclusion holds for a nonlinear perturbation of this equation provided the linearization has a stable zero equilibrium. The results may be easily and naturally generalized to $n$th order equations, although that generalization is not done here.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 39 (1973), 169-172
- MSC: Primary 34D05
- DOI: https://doi.org/10.1090/S0002-9939-1973-0313596-9
- MathSciNet review: 0313596