caa a22 4500 60619391X CHVBK 20210128100911.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s00030-015-0345-y doi (NATIONALLICENCE)springer-10.1007/s00030-015-0345-y Liouville-type theorems for a quasilinear elliptic equation of the Hénon-type [Elektronische Daten] [Quoc Phan, Anh Duong] We consider the Hénon-type quasilinear elliptic equation $${-\Delta_m u=|x|^a u^p}$$ - Δ m u = | x | a u p where $${\Delta_m u={\rm div}(|\nabla u|^{m-2} \nabla u)}$$ Δ m u = div ( | ∇ u | m - 2 ∇ u ) , m>1, p>m − 1 and $${a\geq 0}$$ a ≥ 0 . We are concerned with the Liouville property, i.e. the nonexistence of positive solutions in the whole space $${{\mathbb R}^N}$$ R N . We prove the optimal Liouville-type theorem for dimension N<m+1 and give partial results for higher dimensions. Springer Basel, 2015 Quasilinear nationallicence Liouville-type theorem nationallicence Hénon-typeequation nationallicence Phan Quoc Institute of Research and Development, Duy Tan University, Da Nang, Vietnam aut Duong Anh Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy Street, Cau Giay District, Hanoi, Vietnam aut Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/6(2015-12-01), 1817-1829 1021-9722 22:6<1817 2015 22 30 https://doi.org/10.1007/s00030-015-0345-y text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00030-015-0345-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Phan Quoc Institute of Research and Development, Duy Tan University, Da Nang, Vietnam aut NATIONALLICENCE 700 1- Duong Anh Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy Street, Cau Giay District, Hanoi, Vietnam aut NATIONALLICENCE 773 0- Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/6(2015-12-01), 1817-1829 1021-9722 22:6<1817 2015 22 30