Bulletin of the Australian Mathematical Society

Research Article

Multiplicity of positive periodic solutions to second order differential equations

Jifeng Chua1, Xiaoning Lina2, Daqing Jianga3, Donal O'Regana4 and R. P. Agarwala5

a1 Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

a2 Department of Mathematics, Northeast Normal University, Changchun 130024, Jilin, China

a3 Department of Mathematical Science, Florida Institute of Technology, Melbourne, FL 32901–6975, United States of America

a4 Department of Mathematics, Northeast Normal University, Changchun 130024, Jilin, China

a5 Department of Mathematics, National University of Ireland, Galway, Ireland

In this paper, we study the existence of positive periodic solutions to the equation x = f (t, x). It is proved that such a equation has more than one positive periodic solution when the nonlinearity changes sign. The proof relies on a fixed point theorem in cones.

(Received August 30 2005)