Abstract
We consider the Hénon-type quasilinear elliptic equation \({-\Delta_m u=|x|^a u^p}\) where \({\Delta_m u={\rm div}(|\nabla u|^{m-2} \nabla u)}\), m > 1, p > m − 1 and \({a\geq 0}\). We are concerned with the Liouville property, i.e. the nonexistence of positive solutions in the whole space \({{\mathbb R}^N}\). We prove the optimal Liouville-type theorem for dimension N < m + 1 and give partial results for higher dimensions.
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Phan, Q.H., Duong, A.T. Liouville-type theorems for a quasilinear elliptic equation of the Hénon-type. Nonlinear Differ. Equ. Appl. 22, 1817–1829 (2015). https://doi.org/10.1007/s00030-015-0345-y
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DOI: https://doi.org/10.1007/s00030-015-0345-y