Sign-preserving solutions for a class of asymptotically linear systems of second-order ordinary differential equations

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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.
Lingua originaleEnglish
pagine (da-a)1-29
Numero di pagine29
RivistaTopological Methods in Nonlinear Analysis
Stato di pubblicazionePublished - 2021

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