We consider sign changing solutions of the equation - Δm (u) = | u |p - 1 u in possibly unbounded domains or in RN. We prove Liouville type theorems for stable solutions or for solutions which are stable outside a compact set. The results hold true for m > 2 and m - 1 < p < pc (N, m). Here pc (N, m) is a new critical exponent, which is infinity in low dimension and is always larger than the classical critical one.
Liouville results for m-Laplace equations of Lane–Emden–Fowler type / L. Damescelli, A. Farina, B. Scinzi, E. Valdinoci. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - 26:4(2009 Jul), pp. 1099-1119.
Liouville results for m-Laplace equations of Lane–Emden–Fowler type
E. ValdinociUltimo
2009
Abstract
We consider sign changing solutions of the equation - Δm (u) = | u |p - 1 u in possibly unbounded domains or in RN. We prove Liouville type theorems for stable solutions or for solutions which are stable outside a compact set. The results hold true for m > 2 and m - 1 < p < pc (N, m). Here pc (N, m) is a new critical exponent, which is infinity in low dimension and is always larger than the classical critical one.
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