Stability of periodic solutions for Lipschitz systems obtained via the averaging method
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- by Adriana Buică and Aris Daniilidis PDF
- Proc. Amer. Math. Soc. 135 (2007), 3317-3327 Request permission
Abstract:
Existence and asymptotic stability of the periodic solutions of the Lipschitz system $x’ (t)=\varepsilon F(t,x,\varepsilon )$ is hereby studied via the averaging method. The traditional $C^{1}$ dependence of $F(s,\cdot ,\varepsilon )$ on $z$ is relaxed to the mere strict differentiability of $F(s,\cdot ,0)$ at $z=z_{0}$ for $\varepsilon =0$, giving room to potential applications for structured nonsmooth systems.References
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Additional Information
- Adriana Buică
- Affiliation: Department of Applied Mathematics, Babeş-Bolyai University, Cluj-Napoca 400084, Romania
- Email: abuica@math.ubbcluj.ro
- Aris Daniilidis
- Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra 08193, Spain
- MR Author ID: 613204
- Email: arisd@mat.uab.es
- Received by editor(s): August 1, 2006
- Published electronically: May 17, 2007
- Additional Notes: The first author was supported by the “Agence universitaire de la Francophonie” (France)
The second author was supported by the MEC Grant No. MTM2005-08572-C03-03 (Spain) - Communicated by: Carmen C. Chicone
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 3317-3327
- MSC (2000): Primary 34C29, 34C25; Secondary 49J52
- DOI: https://doi.org/10.1090/S0002-9939-07-08929-0
- MathSciNet review: 2322764