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Pàgina inicial > Articles > Articles publicats > A Note on Forced Oscillations in Differential Equations with Jumping Nonlinearities |
Data: | 2015 |
Resum: | The goal of this paper is to study bifurcations of asymptotically stable 2-periodic solutions in the forced asymmetric oscillator u c u u a u^ =1 t by means of a Lipschitz generalization of the second Bogolubov's theorem due to the authors. The small parameter >0 is introduced in such a way that any solution of the system corresponding to =0 is 2-periodic. We show that exactly one of these solutions whose amplitude is ^2 c^2 generates a branch of 2-periodic solutions when >0 increases. The solutions of this branch are asymptotically stable provided that c>0. |
Ajuts: | Ministerio de Ciencia e Innovación MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 European Commission 318999 European Commission 316338 |
Nota: | Agraïments: The first author is supported by a grant of the Romanian National Authority for Scientific Research, CNCS UEFISCDI, project number PN-II-ID-PCE-2011- 3-0094. The third author is partially supported by RFBR Grant 13-01-00347. We thank the referees for useful comments which improved our note. |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Matèria: | Asymptotic stability ; Jumping nonlinearity ; Method of averaging ; Periodic solutions |
Publicat a: | Differential Equations and Dynamical Systems, Vol. 23 Núm. 4 (2015) , p. 415-421, ISSN 0974-6870 |
Postprint 7 p, 318.1 KB |