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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On perturbation of unstable second order linear differential equations


Authors: L. Hatvani and L. Pintér
Journal: Proc. Amer. Math. Soc. 61 (1976), 36-38
MSC: Primary 34D10
MathSciNet review: 0422784
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Abstract: In connection with a conjecture of J. M. Bownds, conditions will be given on the fundamental system of the solutions of the unstable differential equation $ y'' + a(t)y = 0$ which assure that the differential equation $ x'' + a(t)x = g(t,x,x')$ has a solution with the property

$\displaystyle \lim \sup (\vert x(t)\vert + \vert x'(t)\vert) = \infty \quad {\text{as }}t \to \infty ,$

provided that $ g(t,x,x')$ is ``sufficiently small".

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DOI: https://doi.org/10.1090/S0002-9939-1976-0422784-5
Keywords: Perturbation, stability, instability, conditional stability
Article copyright: © Copyright 1976 American Mathematical Society