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
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.