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January  1997, 3(1): 25-34. doi: 10.3934/dcds.1997.3.25

Multiple periodic solutions of second order equations with asymmetric nonlinearities

C. Rebelo 1,

1. 

SISSA, via Beirut 2-4, 34013, Trieste, Italy

Received  November 1995 Published  October 1996

The problem of the existence and multiplicity of periodic (harmonic and subharmonic) solutions to the parameter-dependent second order equation $x' '+g(x)=s+w(t)$ is investigated for $|s|$ large under suitable "jumping" conditions on $g'(\pm\infty)$. The results which are obtained complete and complement some recent theorems on the periodic Ambrosetti-Prodi problem.
Keywords: Periodic solutions, asymmetric nonlinearities, Poincaré-Birkhoff fixed point theorem., subharmonics.
Mathematics Subject Classification: Primary: 34C25; Secondary: 34B1.
Citation: C. Rebelo. Multiple periodic solutions of second order equations with asymmetric nonlinearities. Discrete and Continuous Dynamical Systems, 1997, 3 (1) : 25-34. doi: 10.3934/dcds.1997.3.25
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