Stable solutions of $-\Delta u =f(u)$ in $\mathbf R^N$

Louis Dupaigne (1, 2, 3, 4) , Alberto Farina (1)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée
2 ICJ - Institut Camille Jordan
3 EDPA - Équations aux dérivées partielles, analyse
4 UCBL - Université Claude Bernard Lyon 1

The paper proves Liouville-type results for stable solutions of semilinear elliptic PDEs with convex nonlinearity, posed on the entire Euclidean space. Extensions to solutions which are stable outside a compact set are also presented.

Domaines: Equations aux dérivées partielles [math.AP]

Louis Dupaigne, Alberto Farina. Stable solutions of $-\Delta u =f(u)$ in $\mathbf R^N$. 2008. ⟨hal-00288530⟩