Nonexistence of positive supersolutions to some nonlinear elliptic problems

作者：Alarcon S^*; Garcia Melian J; Quaas A

来源：Journal de Mathematiques Pures et Appliquees, 2013, 99(5): 618-634.

DOI：10.1016/j.matpur.2012.10.001

• Nonlinear elliptic problems
• Liouville type theorems
• Comparison principle

In this paper we obtain Liouville type theorems for positive supersolutions of the elliptic problem -Delta u + vertical bar del u vertical bar(q) = lambda f(u) in exterior domains of R-N. Here q %26gt; 1 and the function f can be compared with a power p near zero or infinity. We show that positive supersolutions do not exist in some ranges of the parameters p and q which turn out to be optimal for the model case f(s) = s(p). The related problem -Delta u - vertical bar del u vertical bar(q) = f(u) is also analyzed.

• 出版日期2013-5