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2022 Sign-preserving solutions for a class of asymptotically linear systems of second-order ordinary differential equations
Francesca Dalbono
Topol. Methods Nonlinear Anal. 59(1): 163-191 (2022). DOI: 10.12775/TMNA.2021.023

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.

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Francesca Dalbono. "Sign-preserving solutions for a class of asymptotically linear systems of second-order ordinary differential equations." Topol. Methods Nonlinear Anal. 59 (1) 163 - 191, 2022. https://doi.org/10.12775/TMNA.2021.023

Information

Published: 2022
First available in Project Euclid: 23 March 2022

Digital Object Identifier: 10.12775/TMNA.2021.023

Keywords: asymptotically linear , Morse index , phase angles , planar systems , sign-preserving solutions

Rights: Copyright © 2022 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.59 • No. 1 • 2022
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