Some notes on periodic systems with linear part at resonance

D. Ruiz; J. R. Ward

doi:10.3934/dcds.2004.11.337

Article Contents

2004, Volume 11, Issue 2&3: 337-350. Doi: 10.3934/dcds.2004.11.337

This issue Previous Article Coupled map lattices without cluster expansion Next Article Asymptotic regularity of solutions of singularly perturbed damped wave equations with supercritical nonlinearities

Some notes on periodic systems with linear part at resonance

D. Ruiz^1, and
J. R. Ward^2,

1.
Departamento de Análisis Matemático, Universidad de Granada, 18071 Granada
2.
Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL, 35294-1170

Received: December 31, 2002

Revised: September 30, 2003

Published: August 2004

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Abstract

The existence of $T$-periodic solutions is obtained for second order systems of ordinary differential equations of the form

$u''(t) + g(u(t)) = p(t).$

Most of the results assume that $g\in C(\mathbb R^N, \mathbb R^N)$ is bounded or sublinear. The main theorem unifies previous results and implies several new ones.

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Mathematics Subject Classification: 34B15, 34C25.

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