Periodic solutions of resonant systems with rapidly rotating nonlinearities

Pages: 373 - 383, Volume 31, Issue 2, October 2011

doi:10.3934/dcds.2011.31.373       Abstract        References        Full Text (388.5K)       Related Articles

Pablo Amster - Departamento de Matemática, Universidad de Buenos Aires and CONICET, Ciudad Universitaria, Pabellón I, (1428) Buenos Aires, Argentina (email)
Mónica Clapp - Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, C.U., 04510 México D.F., Mexico (email)

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 $g$.

Keywords:  Nonlinear systems, periodic solutions, rapidly rotating nonlinearities, resonant problems, Leray-Schauder degree.
Mathematics Subject Classification:  Primary: 34B15; Secondary: 34C25.

Received: June 2010;      Revised: October 2010;      Published: June 2011.

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