A multiplicity result for orthogonal geodesic chords in Finsler disks

Dario Corona

doi:10.3934/dcds.2021079

Article Contents

2021, Volume 41, Issue 11: 5329-5357. Doi: 10.3934/dcds.2021079

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for the 1D semilinear damped wave equation on a bounded domain

A multiplicity result for orthogonal geodesic chords in Finsler disks

Dario Corona^,

Università di Camerino, Scuola di Scienze e Tecnologie, Camerino (MC), Italy

^* Corresponding author: Dario Corona
^* Corresponding author: Dario Corona

Received: July 31, 2020

Revised: February 28, 2021

Early access: May 2021

Published: November 2021

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Abstract

In this paper, we study the existence and multiplicity problems for orthogonal Finsler geodesic chords in a manifold with boundary which is homeomorphic to a $ N $-dimensional disk. Under a suitable assumption, which is weaker than convexity, we prove that, if the Finsler metric is reversible, then there are at least $ N $ orthogonal Finsler geodesic chords that are geometrically distinct. If the reversibility assumption does not hold, then there are at least two orthogonal Finsler geodesic chords with different values of the energy functional.

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Mathematics Subject Classification: Primary: 70G75, 70H03, 58E10, 53B40.

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