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

Abstract

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.

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Correspondence to Francesca Dalbono.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Dalbono, F., McKenna, P. Multiplicity results for a class of asymmetric weakly coupled systems of second-order ordinary differential equations. Bound Value Probl 2005, 702485 (2005). https://doi.org/10.1155/BVP.2005.129

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