{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:24:57Z","timestamp":1760239497803,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2020,11,20]],"date-time":"2020-11-20T00:00:00Z","timestamp":1605830400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Consider a compact manifold with boundary, homeomorphic to the N-dimensional disk, and a Tonelli Lagrangian function defined on the tangent bundle. In this paper, we study the multiplicity problem for Euler-Lagrange orbits that satisfy the conormal boundary conditions and that lay on the boundary only in their extreme points. In particular, for suitable values of the energy function and under mild hypotheses, if the Tonelli Lagrangian is reversible then the minimal number of Euler-Lagrange orbits with prescribed energy that satisfies the conormal boundary conditions is N. If L is not reversible, then this number is two.<\/jats:p>","DOI":"10.3390\/sym12111917","type":"journal-article","created":{"date-parts":[[2020,11,23]],"date-time":"2020-11-23T11:50:34Z","timestamp":1606132234000},"page":"1917","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A New Approach for Euler-Lagrange Orbits on Compact Manifolds with Boundary"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7575-710X","authenticated-orcid":false,"given":"Dario","family":"Corona","sequence":"first","affiliation":[{"name":"School of Science and Technology, University of Camerino, 62032 Camerino, (MC), Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5610-471X","authenticated-orcid":false,"given":"Fabio","family":"Giannoni","sequence":"additional","affiliation":[{"name":"School of Science and Technology, University of Camerino, 62032 Camerino, (MC), Italy"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"507","DOI":"10.2307\/1971185","article-title":"Periodic orbits for convex hamiltonian systems","volume":"108","author":"Weinstein","year":"1978","journal-title":"Ann. 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