{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,27]],"date-time":"2026-06-27T09:39:24Z","timestamp":1782553164484,"version":"3.54.5"},"reference-count":30,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,12,5]],"date-time":"2024-12-05T00:00:00Z","timestamp":1733356800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper deals with the second-order semi-linear degenerate elliptic equation yuyy+buy+\u0394xu+|u|\u03b1\u22121u=0,(x,y)\u2208Rn\u00d7(0,\u221e), where n\u22651,\u03b1&gt;1. We establish a Liouville theorem of stable solution of the degenerate equation mentioned above by using the energy method. The classification results for stable solutions belonging to C2 can be thought of as an analogue of the recent results of Farina for the Lane\u2013Emden equation.<\/jats:p>","DOI":"10.3390\/axioms13120856","type":"journal-article","created":{"date-parts":[[2024,12,5]],"date-time":"2024-12-05T08:33:51Z","timestamp":1733387631000},"page":"856","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Stable Solutions of a Class of Degenerate Elliptic Equations"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-1278-2289","authenticated-orcid":false,"given":"Yin","family":"Lang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hairong","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1088","DOI":"10.1016\/j.jfa.2013.08.021","article-title":"Monotonicity and nonexistence results to cooperative systems in the half space","volume":"266","author":"Chen","year":"2014","journal-title":"J. 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