https://hal-u-picardie.archives-ouvertes.fr/hal-03621405Farina, AlbertoAlbertoFarinaLAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352 - UPJV - Université de Picardie Jules Verne - CNRS - Centre National de la Recherche ScientifiqueHasegawa, ShoichiShoichiHasegawaLiouville-type theorems and existence results for stable solutions to weighted Lane-Emden equationsHAL CCSD2020[MATH] Mathematics [math]DESSAIVRE, Louise2022-03-28 10:56:552023-03-01 09:34:082022-03-28 10:56:55enJournal articles10.1017/prm.2018.1601We devote this paper to proving non-existence and existence of stable solutions to weighted Lane-Emden equations on the Euclidean space Double-struck capital R-N, N > 2. We first prove some new Liouville-type theorems for stable solutions which recover and considerably improve upon the known results. In particular, our approach applies to various weighted equations, which naturally appear in many applications, but that are not covered by the existing literature. A typical example is provided by the well-know Matukuma's equation. We also prove an existence result for positive, bounded and stable solutions to a large family of weighted Lane-Emden equations, which indicates that our Liouville-type theorems are somehow sharp.