Multiple periodic solutions of second order equations with asymmetric nonlinearities

C. Rebelo

doi:10.3934/dcds.1997.3.25

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1997, Volume 3, Issue 1: 25-34. Doi: 10.3934/dcds.1997.3.25

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Multiple periodic solutions of second order equations with asymmetric nonlinearities

C. Rebelo^1,

1.
SISSA, via Beirut 2-4, 34013, Trieste

Received: November 1995

Published: January 1997

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Abstract

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.

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Mathematics Subject Classification: Primary: 34C25; Secondary: 34B15.

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