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.
Dalbono Francesca (2022). Sign-preserving solutions for a class of asymptotically linear systems of second-order ordinary differential equations. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 59(1), 163-191 [10.12775/TMNA.2021.023].
Sign-preserving solutions for a class of asymptotically linear systems of second-order ordinary differential equations
Dalbono Francesca
2022-03-06
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.File | Dimensione | Formato | |
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