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On the retarded Liénard equation


Author: Bo Zhang
Journal: Proc. Amer. Math. Soc. 115 (1992), 779-785
MSC: Primary 34K20; Secondary 34D20, 34D40, 34K15
MathSciNet review: 1094508
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Abstract: We consider the equation $ x'' + f(x)x' + g(x(t - h)) = 0$ in which $ f,g$ are continuous with $ f(x) > 0$ for $ x \in R,h$ is a nonnegative constant, and $ xg(x) > 0$ if $ \vert x\vert \geq k$ for some $ k \geq 0$. Necessary and sufficient conditions are given for boundedness of all solutions and their derivatives. When $ k = 0$ we give necessary and sufficient conditions for all solutions and their derivatives to converge to zero.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1094508-1
Keywords: Necessary and sufficient conditions, boundedness and global asymptotic stability
Article copyright: © Copyright 1992 American Mathematical Society