Sign-preserving solutions for a class of asymptotically linear systems of second-order ordinary differential equations
- Authors: Dalbono Francesca
- Publication year: 2022
- Type: Articolo in rivista
- OA Link: http://hdl.handle.net/10447/512225
Abstract
We study multiplicity of solutions to an asymptotically linear Dirichlet problem associated with a planar system of second order ordinary differential equations. The existence of two sign-preserving component-wise solutions is guaranteed when the Morse indexes of the linearizations at zero and at infinity do not coincide, and one of the asymptotic problems has zero-index. The proof is developed in the framework of topological and shooting methods and it is based on a detailed analysis and characterization of the phase angles in a two-dimensional setting.