{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:59:44Z","timestamp":1760151584526,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T00:00:00Z","timestamp":1648684800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004329","name":"Slovenian Research Agency","doi-asserted-by":"publisher","award":["P1-0292, N1-0114, N1-0083"],"award-info":[{"award-number":["P1-0292, N1-0114, N1-0083"]}],"id":[{"id":"10.13039\/501100004329","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We investigate the boundary value problem for biharmonic operators on the Heisenberg group. The inherent features of Hn make it an appropriate environment for studying symmetry rules and the interaction of analysis and geometry with manifolds. The goal of this paper is to prove that a weak solution for a biharmonic operator on the Heisenberg group exists. Our key tools are a version of the Mountain Pass Theorem and the classical variational theory. This paper will be of interest to researchers who are working on biharmonic operators on Hn.<\/jats:p>","DOI":"10.3390\/sym14040705","type":"journal-article","created":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T21:29:15Z","timestamp":1648762155000},"page":"705","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["On Nonlinear Biharmonic Problems on the Heisenberg Group"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5858-063X","authenticated-orcid":false,"given":"Jiabin","family":"Zuo","sequence":"first","affiliation":[{"name":"School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3134-9091","authenticated-orcid":false,"given":"Said","family":"Taarabti","sequence":"additional","affiliation":[{"name":"Information Systems and Technology Engineering Laboratory (LISTI), National School of Applied Sciences, Ibn Zohr University, Agadir 80000, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1480-6983","authenticated-orcid":false,"given":"Tianqing","family":"An","sequence":"additional","affiliation":[{"name":"College of Science, Hohai University, Nanjing 210098, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6643-1271","authenticated-orcid":false,"given":"Du\u0161an D.","family":"Repov\u0161","sequence":"additional","affiliation":[{"name":"Faculty of Education, University of Ljubljana, 1000 Ljubljana, Slovenia"},{"name":"Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia"},{"name":"Institute of Mathematics, Physics and Mechanics, 1000 Ljubljana, Slovenia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,31]]},"reference":[{"key":"ref_1","first-page":"5341","article-title":"Fine grading of sl(p2,C) generated by tensor product of generalized Pauli matrices and its symmetries","volume":"47","author":"Tremblay","year":"2006","journal-title":"J. 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