Multiplicity results for a class of asymmetric weakly coupled systems of second-order ordinary differential equations
© Dalbono and McKenna 2005
Received: 1 November 2004
Published: 12 June 2005
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.