{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,29]],"date-time":"2025-12-29T04:46:25Z","timestamp":1766983585560,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2020,10,23]],"date-time":"2020-10-23T00:00:00Z","timestamp":1603411200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003194","name":"Agent\u00fara Ministerstva \u0160kolstva, Vedy, V\u00fdskumu a \u0160portu SR","doi-asserted-by":"publisher","award":["2\/0127\/20","1\/0358\/20"],"award-info":[{"award-number":["2\/0127\/20","1\/0358\/20"]}],"id":[{"id":"10.13039\/501100003194","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005357","name":"Agent\u00fara na Podporu V\u00fdskumu a V\u00fdvoja","doi-asserted-by":"publisher","award":["APVV-18-0308"],"award-info":[{"award-number":["APVV-18-0308"]}],"id":[{"id":"10.13039\/501100005357","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper presents a method of establishing the D-stability terms of the symmetric solution of scalar symmetric linear and nonlinear functional differential equations. We determine the general conditions of the unique solvability of the initial value problem for symmetric functional differential equations. Here, we show the conditions of the symmetric property of the unique solution of symmetric functional differential equations. Furthermore, in this paper, an illustration of a particular symmetric equation is presented. In this example, all theoretical investigations referred to earlier are demonstrated. In addition, we graphically demonstrate two possible linear functions with the required symmetry properties.<\/jats:p>","DOI":"10.3390\/sym12111761","type":"journal-article","created":{"date-parts":[[2020,10,26]],"date-time":"2020-10-26T03:51:47Z","timestamp":1603684307000},"page":"1761","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["D-Stability of the Initial Value Problem for Symmetric Nonlinear Functional Differential Equations"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5955-9402","authenticated-orcid":false,"given":"Natalia","family":"Dilna","sequence":"first","affiliation":[{"name":"Mathematical Institute of Slovak Academy of Sciences, \u0160tef\u00e1nikova 49, 814 73 Bratislava, Slovakia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7385-6737","authenticated-orcid":false,"given":"Michal","family":"Fe\u010dkan","sequence":"additional","affiliation":[{"name":"Mathematical Institute of Slovak Academy of Sciences, \u0160tef\u00e1nikova 49, 814 73 Bratislava, Slovakia"},{"name":"Department of Mathematical Analysis and Numerical Mathematics, Comenius University, Mlynsk\u00e1 dolina, 842 48 Bratislava, Slovakia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1014-5938","authenticated-orcid":false,"given":"Mykola","family":"Solovyov","sequence":"additional","affiliation":[{"name":"Superconductors Department, Institute of Electrical Engineering, Slovak Academy of Sciences, D\u00fabravsk\u00e1 cesta 9, 841 01 Bratislava, Slovakia"}]}],"member":"1968","published-online":{"date-parts":[[2020,10,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0167-2789(97)00199-1","article-title":"Time-reversal symmetry in dynamical systems: A survey","volume":"112","author":"Lamb","year":"1998","journal-title":"Phys.-Sect. 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