Periodic solutions of resonant systems with rapidly rotating nonlinearities

Pablo Amster; Mónica Clapp

doi:10.3934/dcds.2011.31.373

Article Contents

2011, Volume 31, Issue 2: 373-383. Doi: 10.3934/dcds.2011.31.373

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Periodic solutions of resonant systems with rapidly rotating nonlinearities

Pablo Amster^1, and
Mónica Clapp^2,

1.
Departamento de Matemática, Universidad de Buenos Aires and CONICET, Ciudad Universitaria, Pabellón I, (1428) Buenos Aires
2.
Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, C.U., 04510 México D.F.

Received: June 2010

Revised: October 2010

Published: June 2011

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Abstract

We obtain existence of $T$-periodic solutions to a second order system of ordinary differential equations of the form \[ u^{\prime\prime}+cu^{\prime}+g(u)=p \] where $c\in\mathbb{R},$ $p\in C(\mathbb{R},\mathbb{R}^{N})$ is $T$-periodic and has mean value zero, and $g\in C(\mathbb{R}^{N},\mathbb{R}^{N})$ is e.g. sublinear. In contrast with a well known result by Nirenberg [6], where it is assumed that the nonlinearity $g$ has non-zero uniform radial limits at infinity, our main result allows rapid rotations in $g$.

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

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References

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