Boundary Value Problems
Volume 2005 (2005), Issue 2, Pages 129-151

Multiplicity results for a class of asymmetric weakly coupled systems of second-order ordinary differential equations

Francesca Dalbono1 and P. J. McKenna2

1Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, Torino 10123, Italy
2Department of Mathematics, University of Connecticut, Storrs 06269, CT, USA

Received 1 November 2004

Copyright © 2005 Francesca Dalbono and P. J. McKenna. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We prove the existence and multiplicity of solutions to a two-point boundary value problem associated to a weakly coupled system of asymmetric second-order equations. Applying a classical change of variables, we transform the initial problem into an equivalent problem whose solutions can be characterized by their nodal properties. The proof is developed in the framework of the shooting methods and it is based on some estimates on the rotation numbers associated to each component of the solutions to the equivalent system.