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Periodic Solutions of a Newtonian Equation: Stability by the Third Approximation

✍ Scribed by Rafael Ortega

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
900 KB
Volume
128
Category
Article
ISSN
0022-0396

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✦ Synopsis

This paper presents a sufficient condition for the stability of periodic solutions of a newtonian equation. This condition depends on the third order approximation and does not involve small parameters. An application to an equation with cubic potential is given.

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## Abstract We will find a positive constant Ξ£~2~ such that for any 2__Ο€__ ‐periodic function __h__ (__t__) with zero mean value, the quadratic Newtonian equation __x__ β€³ + __x__^2^ = __Οƒ__ + __h__ (__t__) will have exactly two 2__Ο€__ ‐periodic solutions with one being unstable and another being tw