{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T03:59:22Z","timestamp":1774497562167,"version":"3.50.1"},"reference-count":34,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2013,11,7]],"date-time":"2013-11-07T00:00:00Z","timestamp":1383782400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we develop a general framework for studying Dirichlet Boundary Value Problems (BVP) for second order symmetric implicit differential systems satisfying the Hartman-Nagumo conditions, as well as a certain non-expandability condition. The main result, obtained by means of the equivariant degree theory, establishes the existence of multiple solutions together with a complete description of their symmetric properties. The abstract result is supported by a concrete example of an implicit system respecting D4-symmetries.<\/jats:p>","DOI":"10.3390\/sym5040287","type":"journal-article","created":{"date-parts":[[2013,11,7]],"date-time":"2013-11-07T15:28:06Z","timestamp":1383838086000},"page":"287-312","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Multiple Solutions to Implicit Symmetric Boundary Value Problems for Second Order Ordinary Differential Equations (ODEs): Equivariant Degree Approach"],"prefix":"10.3390","volume":"5","author":[{"given":"Zalman","family":"Balanov","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, University of Texas at Dallas, Richardson, TX 75081, USA"}]},{"given":"Wieslaw","family":"Krawcewicz","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, University of Texas at Dallas, Richardson, TX 75081, USA"}]},{"given":"Zhichao","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, University of Texas at Dallas, Richardson, TX 75081, USA"}]},{"given":"Mylinh","family":"Nguyen","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, University of Texas at Dallas, Richardson, TX 75081, USA"}]}],"member":"1968","published-online":{"date-parts":[[2013,11,7]]},"reference":[{"key":"ref_1","unstructured":"Coddington, E., and Levenson, N. 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