A Note on Forced Oscillations in Differential Equations with Jumping Nonlinearities
Buica, Adriana (Bolyai University. Department of Mathematics)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Makarenkov, Oleg (University of Texas at Dallas. Department of Mathematical Sciences)

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

DOI: 10.1007/s12591-014-0199-5

Postprint 7 p, 318.1 KB

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