# American Institute of Mathematical Sciences

February & 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 & Continuous Dynamical Systems - A, 2004, 11 (2&3) : 337-350. doi: 10.3934/dcds.2004.11.337
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