By the use of the Poincar\'e-Birkhoff fixed point theorem, we prove a multiplicity result for periodic solutions of a second order differential equation, where the nonlinearity exhibits a singularity of repulsive type at the origin and has linear growth at infinity. Our main theorem is related to previous results by Rebelo and Zanolin, in connection with a problem raised by del Pino, Manàsevich and Montero.
A multiplicity result for periodic solutions of second order differential equations with a singularity
BOSCAGGIN, Alberto;
2012-01-01
Abstract
By the use of the Poincar\'e-Birkhoff fixed point theorem, we prove a multiplicity result for periodic solutions of a second order differential equation, where the nonlinearity exhibits a singularity of repulsive type at the origin and has linear growth at infinity. Our main theorem is related to previous results by Rebelo and Zanolin, in connection with a problem raised by del Pino, Manàsevich and Montero.
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