March  2004, 11(2&3): 337-350. doi: 10.3934/dcds.2004.11.337

Some notes on periodic systems with linear part at resonance

1. 

Departamento de Análisis Matemático, Universidad de Granada, 18071 Granada, Spain

2. 

Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL, 35294-1170, United States

Received  January 2003 Revised  October 2003 Published  June 2004

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.

Citation: D. Ruiz, J. R. Ward. Some notes on periodic systems with linear part at resonance. Discrete and Continuous Dynamical Systems, 2004, 11 (2&3) : 337-350. doi: 10.3934/dcds.2004.11.337
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